# Quantitative Methods Linear/Integer Programming

_______ 1. Linear programming models have decision variables for measuring the level of activity.

_______ 2. In a transportation problem, a demand constraint for a specific destination represents the amount of product

demanded by a given destination (customer, retail outlet, store).

_______ 3. In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the

different projects.

_______4. The standard form of a linear programming problem requires that fractional relationships between variables are

eliminated or converted where the right-hand-side of the inequality only contains numerical values.

_______5. A systematic approach to model formulation is to first construct the objective function before determining the

decision variables.

_______6. A maximization problem may be characterized by all greater than or equal to constraints.

_______7. A linear programming model consists of decision variables, constraints, but no objective function.

_______8. The output of a linear programming problem from a computer package regarding the values of decision variables

will always be integer and therefore decision variable values never need to be rounded.

_______9. If the original amount of a resource is 15, and the range of feasibility for it can increase by 5, then the amount of the

resource can increase to 20.

_______10. If we are solving a 0-1 integer programming problem, the constraint x1 + x2¬ = 1 is a mutually exclusive constraint.

_______11. Although the output from a computer software package is precise, the optimal values of the decision variables may

not be integer and thus may need to be rounded.

_______12. Although the output from a computer software package is precise, the optimal values of the decision variables may not be integer and thus may need to be rounded.

_______13. A constraint for a linear programming problem can never have a zero as its right-hand-side value.

_______14. Slack variables are only associated with maximization problems.

_______15. The output of a linear programming problem from a computer package regarding the values of decision variables

will always be integer and therefore decision variable values never need to be rounded.

_______16. In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a

less-than-or equal-to constraint ( <=).

_______17. 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 can not be selected

_______18. 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 can not be selected

_______19. If we are solving a 0-1 integer programming problem, the constraint x1 <= x2¬ is a conditional constraint.

_______20. In a media selection problem, maximization of audience exposure may not result in maximization of total profit.

_______21. Surplus variables are only associated with minimization problems.

_______22. Surplus variables are only associated with minimization problems.

_______23. The graphical approach to the solution of linear programming problems can solve linear programming problems

with more than two decision variables.

Multiple Choice

Identify the letter of the choice that best completes the statement or answers the question.

_______ 24. Let x1 be the number of units to make and x2 be the number of units to buy. If it costs $1.5 to make a unit and $4 to

buy a unit and 4000 units are needed, what is the objective function?

a. Max 1.5x1 + 4x2

b. Min 1.5x1 + 4x2

c. Min 4000 (x1 + x2)

d. Max 6000x1 + 16000x2

_______ 25. 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. What is the objective function?

a. $2R + $4D

b. $3R + $2D

c. $3D + $2R

d. $4D + $2R

e. $4R + $2D

_______ 26. Let x1 be the number of units to make and x2 be the number of units to buy. If it costs $1.5 to make a unit and $4 to

buy a unit and 4000 units are needed, what is the objective function?

a. Max 1.5x1 + 4x2

b. Min 1.5x1 + 4x2

c. Min 4000 (x1 + x2)

d. Max 6000x1 + 16000x2

e. Min 6000x1 + 16000x2

_______27. ____________ solutions are ones that satisfy all the constraints simultaneously.

a. alternate

b. feasible

c. infeasible

d. optimal

_______ 28. 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

_______ 29. 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. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

a. B = 90, M = 75

b. B = 90, M = 75

c. B = 150, M = 0

d. B = 0, M = 200

_______ 30. If Xab = the production of product a in period b, then to 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

_______ 31. Which of the following is not an integer linear programming problem?

a. pure integer

b. mixed integer

c. 0-1 Integer

d. continuous

_______ 32. Which of the following types of constraints may be found in linear programming formulations?

1. <=

2. =

3. >=

a. 1 and 2

b. 2 and 3

c. 1 and 3

d. all of the above

_______ 33. 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

Complete the following sentences with the appropriate word (just one word).

________________34. In the linear programming formulation of the transshipment problem there is one _________ for each node.

________________35. A ______________is a linear relationship representing a restriction on decision making.

________________36. If we are solving a 0-1 integer programming problem, the constraint x1 = x2¬ is a

______________constraint.

________________37. An ______________ solution violates at least one of the model constraints.

________________38. A slack variable generally represents an unused _____________.

________________39. When formulating a linear programming model on a spreadsheet, the measure of performance is located in

the ___________ cell.

________________40. An example of a ________________ point is a distribution center or warehouse located between plants and

stores.

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