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 – 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 5x² + 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