Posted: July 30th, 2022

MAT 540 Week 5 Quiz 3

1. The terms in the objective function or constraints are not additive. TRUE/ FALSE

2. A feasible solution violates at least one of the constraints. TRUE/ FALSE

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

a. 1A + 2B

b. 1A + 2B = 3

c. 1A + 2B > 3

d. 1A + 2B < 3

4. In a linear programming problem, a valid objective function can be represented as

A) Max Z = 5xy

B) Max Z 5x2 + 2y2

C) Max 3x + 3y + 1/3z

D) Min (x1 + x2) / x3

5. Non-negativity constraints restrict the decision variables to negative values. TRUE/ FALSE

6. A graphical solution is limited to linear programming problems with ___ decision variables

2

7. A constraint is a linear relationship representing a restriction on decision making.

TRUE/ FALSE

8. Linear programming is a model consisting of linear relationships representing a firm’s decisions given an objective and resource constraints. TRUE/ FALSE

9. Non-negativity constraints

A) restrict the decision variables to zero.

B) restrict the decision variables to positive values

C) restrict the decision variables to negative values

D) do not restrict the sign of the decision variable.

E) both A and B

10. Decision models are mathematical symbols representing levels of activity. TRUE/ FALSE

11. Which of the following could be a linear programming objective function?

A) Z = 1A + 2BC + 3D

B) Z = 1A + 2B + 3C + 4D

C) Z = 1A + 2B / C + 3D

D) Z = 1A + 2B2 + 3D

E) all of the above

12. Decision variables

A) measure the objective function

B) measure how much or how many items to produce, purchase, hire, etc.

C) always exist for each constraint

D) measure the values of each constraint

13. A linear programming model consists of decision variables, constraints, but no objective function. TRUE/ FALSE

14. The region which satisfies all of the constraints in a graphical linear programming problem is called the

A) region of optimality

B) feasible solution space

C) region of non-negativity

D) optimal solution space

15. The _______________ property of linear programming models indicates that the decision variables cannot be restricted to integer values and can take on any fractional value.

A) linearity

B) additive

C) divisibility

D) certainty

E) proportionality

16. The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup 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. What is the time constraint?

A) 2R + 5D ≤ 480

B) 2D + 4R ≤ 480

C) 2R + 3D ≤ 480

D) 3R + 2D ≤ 480

E) 2R + 4D ≤ 480

17. 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 objective function?

Z = $300B + $150M

A) MAX Z = $300B + $100 M

B) MAX Z = $300M + $150 B

C) MAX Z = $300B + $150 M

D) MAX Z = $300B + $500 M

E) MAX Z = $500B + $300 M

18. In a linear programming model, the numberof constraints must be less than the number of decision variables. TRUE/ FALSE

19. Proportionality means the slope of a constraint or objective function line is not constant. TRUE/ FALSE

20. The objective function is a linear relationship reflecting the objective of an operation. TRUE/ FALS

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