# 38 MCQs, True/False and Fill in the blanks on LPP,IPP

TRUE/FALSE

1. A linear programming model consists of decision variables, constraints, but no objective function.

2. In a linear programming model, the number of constraints must be less than the number of decision variables.

3. The values of decision variables are continuous or divisible.

4. All linear programming models exhibit a set of constraints.

5. Graphical solution to linear programming problems has an infinite number of possible objective function lines.

6. The reduced cost (shadow price) for a positive decision variable is 0.

7. 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.

8. The sensitivity range for an objective coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

9. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

10. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

11. The solution value (Z) to the linear programming relaxation of a maximization problem will always be less than or equal to the optimal solution value (Z) of the integer programming maximization problem

12. The solution to the LP relaxation of a maximization integer linear program provides a lower bound for the value of the objective function.

13. If we are solving a 0-1 integer programming problem, the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint.

14. The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

15. The transshipment model is an extension of the transportation model in which intermediate transshipment points are added between the sources and destinations.

FILL IN THE BLANKS

16. An ______________ solution violates at least one of the model constraints.

17. Multiple optimal solutions can occur when the objective function line is __________ to a constraint line.

18. The sensitivity range for an _____________coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

19. In a maximization linear programming problem profit is maximized in the objective function by subtracting cost from ____________.

20. In a problem involving capital budgeting applications, the 0-1 variables designate the ____________ or _____________ of the different projects.

21. In solving an integer linear programming problem, rounding ____ ________ solution values does not guarantee neither an optimal nor a feasible solution.

22. If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________________constraint.

23. An example of a ________________ point is a distribution center or warehouse located between plants and stores.

24. A plant has 4 jobs to be assigned to 4 machines, each machine has different manufacturing times for each product. The production manager wants to determine the optimal assignments of 4 jobs to 4 machines to minimize total manufacturing time. This problem can be most efficiently solved using the ________________ model.

MULTIPLE CHOICE

25. The minimization of cost or maximization of profit is the

a. objective of a business

b. constraint of operations management

c. goal of management science

d. objective of linear programming

e. both a and d

26. Cully 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. What is the storage space constraint?

a. 90B + 100M>= 18000

b. 90B + 100M <= 18000

c. 100B + 90M <= 18000

d. 500B + 300M<= 18000

e. 300B + 500M <= 18000

27. The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. Which of the following is not a feasible production combination? Please show complete work. Only answer carries no marks.

a. 90R and 75D

b. 135R and 0D

c. 0R and 120D

d. 75R and 90D

e. 40R and 100D

28. 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. If the Mallory Furniture company decides to purchase 150 big shelves and no medium shelves, which of the two resources will be left over? Please show complete work. Only answer carries no marks.

a. investment money only

b. storage space only

c. investment money and storage space

d. neither investment money nor storage space

29. Which of the following could not be a linear programming problem constraint?

a. 1A + 2B < 5

b. 1A + 2B <= 3

c. 1A + 2B = 3

d. 1A + 2B + 3C + 4D<= 5

e. 1A + 3B >= 6

30. Given the following linear programming problem:

Min Z = 2x + 8y

Subject to (1) 8x + 4y>= 64

(2) 2x + 4y>= 32

(3) y >= 2

Please show complete work.

At the optimal solution the minimum cost is:

a. $30

b. $40

c. $50

d. $52

d. $53.33

31. 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? Please show complete work.

a. chicken, mashed potatoes and gravy, jello and salad

b. lasagna, mashed potatoes and gravy, and jello

c. chicken, mashed potatoes and gravy, and pudding

d. lasagna, mashed potatoes and gravy, and salad

e. chicken, mashed potatoes and gravy, and salad

32. 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 ______________.

a. problem constraints, sales

b. problem constraints, profits

c. objective function, profits

d. problem output, marginal revenue

e. problem statement, revenue

33. If Xab = the production of product a in period b, then indicate that the limit on production of the company's "3" products in period 2 is 400.

a. X32 400

b. X21 + X22 + X23<= 400

c. X12 + X22 + X32<= 400

d. X12 + X22 + X32 <= 400

e. X23<= 400

34. Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1.

a. x11 + x12<= (.35)(x11 + x21)

b. x11>= .35 (x11 + x21)

c. x11<= .35 (x11 + x12)

d. -.65x11 + .35x21 <=0

e. .65x11 - .35x21<= 0

35. Let: rj = regular production quantity for period j, oj =overtime production quantity in period j, ii = inventory quantity in period j, and di = demand quantity in period j

Correct formulation of the demand constraint for a multi-period scheduling problem is:

a. rj + oj + i2 - i1 >= di

b. rj + oj + i1 - i2 >= di

c. rj + oj + i1 - i2 <= di

d. rj - oj - i1 + i2 >= di

e. rj + oj + i2 - i1 <= di

36. Which of the following is not an integer linear programming problem?

a. pure integer

b. mixed integer

c. 0-1integer

d. continuous

37. If we are solving a 0-1 integer programming problem, the constraint x1<= x2 is a ________________constraint.

a. multiple choice

b. mutually exclusive

c. conditional

d. corequisite

e. none of the above

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#### Solution Preview

TRUE/FALSE

1. A linear programming model consists of decision variables, constraints, but no objective function.

2. In a linear programming model, the number of constraints must be less than the number of decision variables.

3. The values of decision variables are continuous or divisible.

4. All linear programming models exhibit a set of constraints.

5. Graphical solution to linear programming problems has an infinite number of possible objective function lines.

6. The reduced cost (shadow price) for a positive decision variable is 0.

7. 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.

8. The sensitivity range for an objective coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

9. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

10. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

11. The solution value (Z) to the linear programming relaxation of a maximization problem will always be less than or equal to the optimal solution value (Z) of the integer programming maximization problem

12. The solution to the LP relaxation of a maximization integer linear program provides a lower bound for the value of the objective function.

13. If we are solving a 0-1 integer programming problem, the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint.

14. The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

15. The transshipment model is an extension of the transportation model in which intermediate transshipment points are added between the sources and destinations.

FILL IN THE BLANKS

16. An ______________ solution violates at least one of the model constraints.

17. Multiple optimal solutions can occur when the objective function line is __________ to a constraint line.

18. The sensitivity range for an _____________coefficient is the range of values over which ...

#### Solution Summary

This posting contains answers with explainations to 39 MCQs, True/False and Fill in the blanks