Question

Market Insights Co. (MIC) is a full-service market research company. MIC is being hired to interview registered voters in a district to gain insight into their opinions about certain 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 as follows:

	Cost Per Interview
Gender	Democrat	Republican	Independent
Male	$ 10	$ 9	$ 13
Female	$ 12	$ 11	$ 14

The contract called for MIC to conduct interviews under the guidelines given below. MIC’s goal is to develop an interview plan that will satisfy the contract requirements at a minimum total interview cost.

Part 1. Linear Programming (LP) Model

Please formulate a linear programming (LP) model. Please follow the steps below.

Define the decision variables.

Write the objective.

Write the constraints (which are the contract requirements).

There must be at least 4,500 total interviews.

At least 1,000 Independent voters must be interviewed.

At least 2,000 males must be interviewed.

At least 1,750 females must be interviewed.

No more than 40% of those interviewed may be Democrats.

No more than 35% of those interviewed may be Republicans.

No more than 25% of those interviewed may be Republican males.

Each of the six types of voters must be represented by at least 10% of the total interviews.

Constraints on decision variables.

Answer 1