Linear Programming Applications
MULTIPLE CHOICE
1. Media selection problems usually determine
a. how many times to use each media source.
b. the coverage provided by each media source.
c. the cost of each advertising exposure.
d. the relative value of each medium.
2. A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD = 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know?
a. the objective function coefficient of HD is 10.
b. the dual price for the HD constraint is 10.
c. the objective function coefficient of HD is -10.
d. the dual price for the HD constraint is -10.
3. Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is
a. Max 2M + 3B
b. Min 4000 (M + B)
c. Max 8000M + 12000B
d. Min 2M + 3B
4. Let Pij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units,
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a.
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P13 - P14 = 100; P14 - P13 = 100
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b.
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P13 - P14 = 100; P13 - P14 = 100
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c.
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P13 - P14 = 10; P14 - P13 = 10
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d.
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P13 - P14 = 1000; P14 - P13 = 1000
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5. Department 3 has 2500 hours. Transfers are allowed to departments 2 and 4, and from departments 1 and 2. If Ai measures the labor hours allocated to department i and Tij the hours transferred from department i to department j, then
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a.
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T13 + T23 - T32 - T34 - A3 = 2500
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b.
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T31 + T32 - T23 - T43 + A3 = 2500
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c.
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A3 + T13 + T23 - T32 - T34 = 2500
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d.
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A3 - T13 - T23 + T32 + T34 = 2500
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PROBLEM
6.A&C Distributors is a company that represents many outdoor products companies and schedules deliveries to discount stores, garden centers, and hardware stores. Currently, scheduling needs to be done for two lawn sprinklers, the Water Wave and Spring Shower models. Requirements for shipment to a warehouse for a national chain of garden centers are shown below.
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Month
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Shipping Capacity
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Product
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Minimum Requirement
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Unit Cost
to Ship
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Per Unit
Inventory Cost
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March
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8000
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Water Wave
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3000
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.30
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.06
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Spring Shower
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1800
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.25
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.05
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April
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7000
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Water Wave
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4000
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.40
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.09
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Spring Shower
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4000
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.30
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.06
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May
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6000
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Water Wave
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5000
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.50
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.12
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Spring Shower
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2000
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.35
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.07
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Let Sij be the number of units of sprinkler i shipped in month j, where i = 1 or 2, and j = 1, 2, or 3. Let Wij be the number of sprinklers that are at the warehouse at the end of a month, in excess of the minimum requirement.
6. Write the portion of the objective function that minimizes shipping costs.
a. Min .3S11 + .25S21 + .40S12 + .30S22 + .50S13 + .35S23
b. Min .06W11 + .05W21 + .09W12 + .06W22 + .12W13 + .07W23
c. Min .25S11 + .3S21 + .40S12 + .50S22 + .30S13 + .35S23
d. Min .16W11 + .05W21 + .09W12 + .16W22 + .12W13 + .07W23
7. An inventory cost is assessed against this ending inventory. Give the portion of the objective function
that represents inventory cost.
a. Min .3S11 + .25S21 + .40S12 + .30S22 + .50S13 + .35S23
b. Min .06W11 + .05W21 + .09W12 + .06W22 + .12W13 + .07W23
c. Min .25S11 + .3S21 + .40S12 + .50S22 + .30S13 + .35S23
d. None of the above
8. There will be three constraints that guarantee, for each month, that the total number of sprinklers shipped will not exceed the shipping capacity. These are
a. S11 + S21 = < 8000, S12 + S22 = < 6000, S13 + S23 = < 7000
b. S11 + S22 = < 8000, S12 + S22 = < 7000, S11 + S23 = < 6000
c. S11 + S21 = < 8000, S12 + S22 = < 7000, S13 + S23 =< 6000
d. S33 + S21 = < 8000, S12 + S22 =< 7000, S11 + S23 = < 6000
9. There are six constraints that work with inventory and the number of units shipped, making sure that enough sprinklers are shipped to meet the minimum requirements. Write these six constraints
a.
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S21 - W11 = 3000
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S11 - W21 = 1800
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W11 + S22 - W12 = 4000
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W21 + S22 - W22 = 4000
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W12 + S13 - W13 = 5000
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W22 + S23 - W23 = 2000
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b.
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S11 - W11 = 3000
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S21 - W21 = 1800
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W11 + S12 - W12 = 4000
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W21 + S22 - W22 = 4000
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W12 + S13 - W13 = 5000
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W22 + S23 - W23 = 2000
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c.
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S11 - W11 = 3000
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S21 - W21 = 1800
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W11 - W12 = 4000
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W21 + S22 - W22 = 4000
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W12 + S13 - W13 = 5000
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W22 + S23 - W23 = 2000
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d. None of the above
From Previous Chapters
10-. To solve a linear programming problem with thousands of variables and constraintsa. a personal computer can be used.
b. a mainframe computer is required.
c. the problem must be partitioned into subparts.
d. unique software would need to be developed.