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MAT 540 FINAL EXAM THREE VERSIONS (120 QUESTIONS)
NOTE: PLEASE IF SOME OF YOUR QUESTIONS IS DIFFERENT FROM THIS, MESSAGE ME I WILL PROVIDE ANSWER FOR FREE. YOU HAVE 5HRS FOR THE EXAM
Question 1   Validation of a simulation model occurs when the true steady state average results have been reached. Answer  True  False Question 2   In a total integer model, all decision variables have integer solution values.  Answer  True  False Question 3   Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.Answer  True  False Question 4   A cycle is an up and down movement in demand that repeats itself in less than 1 year. Answer  True  False
Question 5   Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.  Answer  True  False Question 6   In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected. Answer  True  False Question 7   In a break-even model, if all of the costs are held constant, how does an increase in price affect the model?Answer   Breakeven point decreases  Breakeven point increases  Breakeven point does not change  The revenue per unit goes down
Question 8   Events that cannot occur at the same time in any trial of an experiment are:Answer   exhaustive  dependent  independent  mutually exclusive
Question 9   A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.                If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:Answer   12  55  57  69
Question 10   A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.                The conservative (maximin) strategy is:Answer   Buy  Rent  Lease  Brisk.
Question 11   The probability of observing xsuccesses in a fixed number of trials is a problem related toAnswer   the normal distribution  the binomial distribution  conditional probability  the Poisson distribution
Question 12   Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased? Answer   B = 225, M = 0  B = 0, M = 225  B = 150, M = 75  B = 75, M = 150
Question 13   Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the objective function?Answer   Max Z = 75B + 85M  Max Z = 85B + 75M  100B + 50M  ≤  25000  100B + 50M  ≥ 25000  100B + 80M  ≤  18000  100B + 80M  ≥  18000
Question 14   The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:   The Answer Report:   The Sensitivity Report:    Which additional resources would you recommend to be increased?Answer   mix/mold  kiln  paint and seal  Cannot tell from the information provided
Question 15   Given the following linear programming problem that minimizes cost. Min Z = 2x + 8y Subject to        8x + 4y ≥ 64                         2x + 4y ≥ 32                         y ≥ 2  What is the sensitivity range for the third constraint, y ≥ 2?Answer   0 to 4  2 to 5.33  0 to 5.33  4 to 6.33
Question 16   The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively.  Five essential ingredients are contained in the feed, shown in the table below.  The table also shows the minimum daily requirements of each ingredient.  Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds)1 20 24 302 30 10 503 0 30 204 24 15 605 10 20 40
 The constraint for ingredient 3 is:Answer   .5A + .75B = 20  .3B = 20  .3 B≤ 20  .3B ≥ 20
Question 17   In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively.  The investor has up to $50,000 to invest.An appropriate part of the model would beAnswer   15X1 + 47.25X2 +110 X3 ≤ 50,000  MAX   Z =15X1 + 47.25X2 + 110X3  X1 + X2 +X3 ≤ 50,000  MAX    Z = 50(15)X1 + 50 (47.25)X2 + 50 (110)X3
Question 18   The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.Answer   Y1 + Y4 ≤ 0  Y1 + Y4 = 0  Y1 + Y4 ≤ 1  Y1 + Y4 ≥ 1
Question 19   The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write the constraint that indicates they have to use at least three of the five machines in their production.Answer   Y1 + Y2 + Y3 + Y4+ Y5  ≤ 3  Y1 + Y2 + Y3 + Y4+ Y5  = 3  Y1 + Y2 + Y3 + Y4+ Y5  ≥ 3  none of the above
Question 20   The assignment problem constraint x31+x32+x33+x34 ≤ 2 meansAnswer   agent 3 can be assigned to 2 tasks  agent 3 can be assigned to no more than 2 tasks  a mixture of agents 1, 2, 3 and 4 will be assigned to tasks  agent 2 can be assigned to 3 tasks
Question 21   The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.                                The constraint that represents the quantity supplied by DC 1 is:Answer   4X1A + 6X1B + 8X1C ≤ 500  4X1A + 6X1B + 8X1C = 500  X1A + X1B + X1C ≤ 500  X1A + X1B + X1C ≥500  Question 22   Jack is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. The decisions of each university have no effect on each other.  This means that they are:Answer   mutually exclusive  independent  controlled by the central limit theorem  all of the above
Question 23   The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport.  At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels.  What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? Note:  please provide your answer to 2 places past the decimal point, rounding as appropriate.  Answer   0.03  0.05  0.07  0.09
Question 24   A bakery is considering hiring another clerk to better serve customers.  To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals.  Based on 100 ten-minute intervals, the following probability distribution and random number assignments developed.   Number of Arrivals Probability Random numbers6 .1 .01 #8211; .107 .3 .11 #8211; .408 .3 .41 #8211; .709 .2 .71 #8211; .9010 .1 .91 #8211; .00
          Suppose the next three random numbers were .18, .89 and .67.  How many customers would have arrived during this 30-minute period?Answer   23  24  22  25
Question 25   Consider the following graph of sales.                          Which of the following characteristics is exhibited by the data?Answer   Trend only  Trend plus seasonal  Trend plus irregular  Seasonal
Question 26   For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:                           Answer   0  1  2  3
Question 27   __________ moving averages react more slowly to recent demand changes than do __________ moving averages.Answer   Longer-period, shorter-period  Shorter-period, longer-period  Longer-period, longer-period  Shorter-period, shorter-period
Question 28   Suppose that a production process requires a fixed cost of $50,000. The variable cost per unit is $10 and the revenue per unit is projected to be $50.  Find the break-even point. Answer 
 
Question 29   Carter’s Bed ; Breakfast breaks even every month if they book 30 rooms over the course of a month.  Their fixed cost is $1050 per month and the revenue they receive from each booked room is $150.  What is the variable cost per occupied room?  (Note: The answer is a whole dollar amount.   Give the answer as a whole number, omitting the decimal point.  For instance, use 105 to write $105.00).  Answer 
 
Question 30   Nixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive from each booked room is $200.  The variable cost per room is $75.  How many rooms do they have to sell each month to break even?  (Note: The answer is a whole number.   Give the answer as a whole number, omitting the decimal point.  For instance, use 12 for twelve rooms).  Answer 
 
 
Question 31   Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):  MAX50R + 75S s.t.              1.2R + 1.6 S ≤ 600 assembly (hours)              0.8R + 0.5 S ≤ 300 paint (hours)              .16R + 0.4 S ≤ 100 inspection (hours)  Sensitivity Report:                  Final Reduced Objective Allowable AllowableCell Name Value Cost Coefficient Increase Decrease$B$7  Regular = 291.67 0.00 50 70 20$C$7 Super = 133.33 0.00 75 50 43.75                              Final Shadow Constraint Allowable AllowableCell Name Value Price R.H. Side Increase Decrease$E$3 Assembly (hr/unit) 563.33 0.00 600 1E+30 36.67$E$4 Paint (hr/unit) 300.00 33.33 300 39.29 175$E$5 Inspect (hr/unit) 100.00 145.83 100 12.94 40
  A change in the market has increased the profit on the super product by $5. Total profit will increase by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign. Answer 
 
Question 32   Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.    Formulation: Let                   x = number of tractors produced per period                         y = number of lawn mowers produced per period MAX 30x + 30y subject to   2 x + y       ≤ 60                   2 x + 3y     ≤ 120                      x ≤ 45                     x, y  ≥ 0The graphical solution is shown below.      What is the shadow price for fabrication?  Write your answers with two significant places after the decimal and do not include the dollar “$” sign. Answer 
 
Question 33   Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows:              Cat Food Cost/oz protien (%) fat (%)Meow Munch $0.20 30 10Feline Feed $0.15 15 30
  Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Note:  Please write your answers with two significant places after the decimal and do not include the dollar “$” sign.  For instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45 Answer 
 
Question 34   Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer. Max Z =         x1 + 6#215;2 Subject to:      17#215;1 + 8#215;2 ≤ 136                        3#215;1 + 4#215;2 ≤ 36                        x1, x2 ≥ 0 and integerAnswer 
 
Question 35   Let’s say that a life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 72 years and a standard deviation of 5 years. What proportion of the plan participants are expected to survive to see their 75thbirthday?   Note:  Round your answer, if necessary, to two places after the decimal.  Please express your answer with two places after the decimal.   Answer 
Question 36   Ms. James is considering four different opportunities, A, B, C, or D.  The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.   Investment Economic Conditions Poor(S1) Average(S2) Good(S3) Excellent(S4)A  18 25 50 80B 19 100 50 75C  100 26 120 60D 20 27 50 240
  Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicableAnswer 
Question 37   The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).  Note:  Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000).  Round to the nearest whole number, if necessary.                             Answer 
Question 38   The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).  Note:  Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000).  Round to the nearest whole number, if necessary.                              Answer 
 
Question 39   The following sales data are available for 2003-2008 :   Year Sales Forecast2003 7 72004 8 8.52005 12 10.52006 14 132007 16 152008 18 16
 Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places.  If necessary, round your result accordingly.  For instance, 9.14677, should be expressed as 9.1468Answer 
Question 40   Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer. Answer 
 
 
Final Draft of MAT 540 Final
1. Which of the following could be a linear programming objective function? (Points : 5)        Z = 1A + 2BC + 3D       Z = 1A + 2B + 3C + 4D       Z = 1A + 2B / C + 3D       Z = 1A + 2B2 + 3D       all of the above
 
2. Which of the following could not be a linear programming problem constraint? (Points : 5)        1A + 2B       1A + 2B = 3       1A + 2B LTOREQ 3       1A + 2B GTOREQ 3
3. Types of integer programming models are _____________. (Points : 5)        total       0 #8211; 1       mixed       all of the above
4. The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. If the production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer, it will result in slack of (Points : 5)        malt only       wheat only       both malt and wheat       neither malt nor wheat
5. The reduced cost (shadow price) for a positive decision variable is 0.  (Points : 5)         True         False
6. Decision variables (Points : 5)        measure the objective function       measure how much or how many items to produce, purchase, hire, etc.       always exist for each constraint       measure the values of each constraint
 
 
7. A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 340 minutes, providing two additional machine hours will result in the: (Points : 5)        same product mix, different total profit       different product mix, same total profit as before       same product mix, same total profit       different product mix, different total profit
8. Decision models are mathematical symbols representing levels of activity.  (Points : 5)         True         False
9. The integer programming model for a transportation problem has constraints for supply at each source and demand at each destination.  (Points : 5)         True         False
10. In a transportation problem, items are allocated from sources to destinations (Points : 5)        at a maximum cost       at a minimum cost       at a minimum profit       at a minimum revenue
11. In a media selection problem, the estimated number of customers reached by a given media would generally be specified in the _________________. Even if these media exposure estimates are correct, using media exposure as a surrogate does not lead to maximization of ______________. (Points : 5)        problem constraints, sales       problem constraints, profits       objective function, profits       problem output, marginal revenue       problem statement, revenue 
12. ____________ solutions are ones that satisfy all the constraints simultaneously. (Points : 5)        alternate       feasible       infeasible       optimal       unbounded
 
 
13. In a linear programming problem, a valid objective function can be represented as (Points : 5)        Max Z = 5xy       Max Z 5#215;2 + 2y2       Max 3x + 3y + 1/3z       Min (x1 + x2) / x3
14. The standard form for the computer solution of a linear programming problem requires all variables to the right and all numerical values to the left of the inequality or equality sign  (Points : 5)         True         False
15. Constraints representing fractional relationships such as the production quantity of product 1 must be at least twice as much as the production quantity of products 2, 3 and 4 combined cannot be input into computer software packages because the left side of the inequality does not consist of consists of pure numbers.  (Points : 5)         True         False
16. In a balanced transportation model where supply equals demand, (Points : 5)        all constraints are equalities       none of the constraints are equalities       all constraints are inequalities       all constraints are inequalities
17. The objective function is a linear relationship reflecting the objective of an operation.  (Points : 5)         True         False
18. The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $0.50. Which of the following is not a feasible production combination? (Points : 5)        0L and 0V       0L and 1000V       1000L and 0V       0L and 1200V
 
19. The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.  (Points : 5)         True         False
20. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: (Points : 5)        same product mix, different total profit       different product mix, same total profit as before       same product mix, same total profit       different product mix, different total profit
21. In a total integer model, all decision variables have integer solution values.  (Points : 5)         True         False
22. Linear programming is a model consisting of linear relationships representing a firm#8217;s decisions given an objective and resource constraints.  (Points : 5)         True         False
23. When using linear programming model to solve the #8220;diet#8221; problem, the objective is generally to maximize profit.  (Points : 5)         True         False
24. In a balanced transportation model where supply equals demand, all constraints are equalities.  (Points : 5)         True         False
25. In a transportation problem, items are allocated from sources to destinations at a minimum cost.  (Points : 5)         True         False
 
 
26. Mallory Furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150.  Which of the following is not a feasible purchase combination? (Points : 5)        0 big shelves and 200 medium shelves       0 big shelves and 0 medium shelves       150 big shelves and 0 medium shelves       100 big shelves and 100 medium shelves
27. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.  (Points : 5)         True         False
28. In a 0 #8211; 1 integer model, the solution values of the decision variables are 0 or 1.  (Points : 5)         True         False
29. Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem.   (Points : 5)         True         False
30. The dietician for the local hospital is trying to control the calorie intake of the heart surgery patients. Tonight#8217;s dinner menu could consist of the following food items: chicken, lasagna, pudding, salad, mashed potatoes and jello. The calories per serving for each of these items are as follows: chicken (600), lasagna (700), pudding (300), salad (200), mashed potatoes with gravy (400) and jello (200). If the maximum calorie intake has to be limited to 1200 calories. What is the dinner menu that would result in the highest calorie in take without going over  the total calorie limit of 1200. (Points : 5)        chicken, mashed potatoes and gravy, jello and salad       lasagna, mashed potatoes and gravy, and jello       chicken, mashed potatoes and gravy, and pudding       lasagna, mashed potatoes and gravy, and salad       chicken, mashed potatoes and gravy, and salad    
31. When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints#8217; prices.    (Points : 5)         True         False
 
 
32. The transportation method assumes that (Points : 5)        the number of rows is equal to the number of columns       there must be at least 2 rows and at least 2 columns       1 and 2       the product of rows minus 1 and columns minus 1 should not be less than the number of completed cells
33. A constraint is a linear relationship representing a restriction on decision making.  (Points : 5)         True         False
34. When formulating a linear programming model on a spreadsheet, the measure of performance is located in the target cell.
  (Points : 5)         True         False
35. The linear programming model for a transportation problem has constraints for supply at each ________ and _________ at each destination. (Points : 5)        destination / source       source / destination       demand / source       source / demand
36. The 3 types of integer programming models are total, 0 #8211; 1, and mixed.  (Points : 5)         True         False
37. In using rounding of a linear programming model to obtain an integer solution, the solution is (Points : 5)        always optimal and feasible       sometimes optimal and feasible       always optimal       always feasible       never optimal and feasible
38. If we use Excel to solve a linear programming problem instead of QM for Windows,then the data input requirements are likely to be much less tedious and time consuming.   (Points : 5)         True         False
39. In a _______ integer model, some solution values for decision variables are integer and others can be non-integer. (Points : 5)        total       0 #8211; 1       mixed       all of the above
40. Which of the following is not an integer linear programming problem? (Points : 5)        pure integer       mixed integer       0-1integer       continuous
 

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