# MAT 540 Week 11 Final Exam (Latest 2016) 2016

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 – 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 constrain

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 5×2 + 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’s decisions given an objective and resource constraints.

(Points : 5)

True

False

23. When using linear programming model to solve the “diet” 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 – 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’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’ 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 – 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 – 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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