Question

8. Management Sciences Associates (MSA) based in Washington, D.C., is a marketing and computer research firm that handles consumer surveys for several clients. One client is a national press service that periodically conducts political polls on issues of widespread interest. In order to draw statistically valid conclusions on the sensitive issue of new U.S. immigration laws, in a survey for the press service, MSA determines that it must a. Survey at least 2,300 U.S. households in total. b. Survey at least 1,000 households whose heads are 30 years of age or younger c. Survey at least 600 households whose heads are between 31-50 years of age d. At least 15 percent of those surveyed must live in a state that borders on Mexico e. No more than 20 percent of those surveyed who are 51 or over can live in states that border on Mexico MSA decides that all surveys should be conducted in person. region category are as follows: It estimates that the costs of reaching people in each age and 9. Surveyed 11. Age 31-50 13. $6.80 16. $7.245 Cost Per Person Region State bordering Mexico State not bordering Mexico 10 12. Age 51 + 14. $5.50 17. $6.10 Age 0-30 $7.50 15. $6.90 MSA's goal is to meet the five sampling requirements at the least possible cost

Answer 1

Decision Variables Number of persons in each category Region State bordering Mexico State not bordering Mexico Objective function Age31-50 Age51+ 4 7 B4*7.5+6.8 CA+D4 5.5+B5 *6.9+C5 7.25+D5 *6.1 Constraints 9 SUM(B4:D5) 10 B4+B5 11 C4+C5 2-SUMB:D4) 2300 1000 600 0.15 SUM(B4:D5) 0.2 (D4+D5) 13:M 14 15

Decision Variables Number of persons in each category Region Age0-30 Age31-50Age51+ 4State bordering Mexico 5 State not bordering Mexico 6 Objective function 0 Constraints C) C) C) C) C) x: x: x: x: 2300 1000 600 C) C) 10 12 13

Solver Parameters Set Objective To: O Max By Changing aiable Cells: SAS기 Value Of: SBS4:SDS5 Subject to the Constraints: SAS13SCS13 SAS9:SAS12SCS9:SCS12 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a SolvingSimplex LP Method: Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Decision Variables Number of persons in each category Region Age0-30 Age31-50 Age51+ 600 0 4 State bordering Mexico 0 140 5 State not bordering Mexico 1000 Objective function 15166 Constraints 2300 2300 10 1000 1000 740 140 12 140