Formulate a linear programming problem for the following scenario. Use the area on the next page to provide your proper formulation for this problem. Make sure you save this “renamed” Word document after you complete your formulation.
Scenario
A political polling organization is to conduct a poll of likely
voters prior to an upcoming election. Each voter is to be
interviewed in person. It is known that the costs of interviewing
different types of voters vary due to the differences in
proportion within the population. The costs to interview males, for
example, are $10 per Democrat, $9 per Republican, and $13.50 per
Independent voter. The costs to interview females are $12, $11 and
$13.50 for Democrat, Republican, and Independent voters,
respectively. The polling service has been given certain criteria
to which it must adhere:
There must be at least 4,500 total interviews.
At least 1,000
independent voters must be polled.
At least 2,000 males must be polled.
At least 1,750 females must be polled.
No more than 40 of those polled may be Republicans.
No more than
one-quarter of those polled may be Republican males.
Each of the six categories of voters must be represented in the
poll by at least 10% of the total interviews.
The objective is to determine the least expensive sampling plan and the total cost to carry out the plan.
Define the decision variables as follows:
M1 = No. of male Democrat
M2 = No. of male Republican
M3 = No. of male Independent voters
F1 = No. of female Democrat
F2 = No. of female Republican
F3 = No. of female Independent voters
Minimize Z = total cost = 10 M1 + 9 M2 + 13.5 M3 + 12 F1 + 11 F2 + 13.5 F3
Subject to,
M1 + M2 + M3 + F1 + F2 + F3 >= 4500
M3 + F3 >= 1000
M1 + M2 + M3 >= 2000
F1 + F2 + F3 >= 1750
M2 + F2 <= 40
M2 <= 1/4 * (M1 + M2 + M3 + F1 + F2 + F3) i.e. M1 - 3 M2 + M3 + F1 + F2 + F3 >= 0
M1 >= 10% * (M1 + M2 + M3 + F1 + F2 + F3) i.e. -0.9 M1 + 0.1 M2 + 0.1 M3 + 0.1 F1 + 0.1 F2 + 0.1 F3 <= 0
Similarly
0.1 M1 - 0.9 M2 + 0.1 M3 + 0.1
F1 + 0.1 F2 + 0.1 F3 <= 0
0.1 M1 + 0.1 M2 - 0.9 M3 + 0.1
F1 + 0.1 F2 + 0.1 F3 <= 0
0.1 M1 + 0.1 M2 + 0.1 M3 - 0.9
F1 + 0.1 F2 + 0.1 F3 <= 0
0.1 M1 + 0.1 M2 + 0.1 M3 + 0.1
F1 - 0.9 F2 + 0.1 F3 <= 0
0.1 M1 + 0.1 M2 + 0.1 M3 + 0.1
F1 + 0.1 F2 - 0.9 F3 <= 0
M1, M2, M3, F1, F2, F3 >= 0
Formulate a linear programming problem for the following scenario. Use the area on the next page...
M3_A5. A political polling organization has been hired to conduct a poll of likely voters prior to an upcoming election. Each voter is to be interviewed in person. It is known that he costs of interviewing different types of voters vary due to the difference in proportion within the population. The costs to interview males, for example, are $20 per Democrat, $18 per Republican, and $27 per Independent voter. The costs to interview female are $24, $22 and $28 for...
JUST NEED HELP WITH PART 2 (EXCEL SOLVER) Clearlake Marketing Group (CMG) is a full-service marketing research company. CMG is being hired to interview registered voters in a city to gain insights into their opinions about certain political issues. Each voter is to be interviewed in person. The costs of interviewing different types of voters vary due to the differences in proportion throughout the population. Based on previous studies, estimates of the interview costs for different types of voters are...
Formulate and solve the following LPs in Excel. Only the first two are provided for now. I will complete the assignment after I return from the conference. Maggie loves desserts, but due to health concerns, she has decided that she must plan carefully. There are two desserts that she is considering: snack bars and ice cream. After reading the nutrition labels, she learns that each serving of the snack bar weighs 137 grams and contains 120 calories and 5 grams...