Marketing Advantage, Inc.

Marketing Advantage, Inc. (MAI) is a full-service market research company. MAI is being hired to interview registered voters in a district to gain insights into their opinions about certain issues. Each voter is to be interviewed in person. The cost of interviewing different types of voters varies due to the differences in proportion throughout the population. Based on previous studies, estimate of the interviewing cost for different types of voters is given below.

	Cost Per Interview
Gender	Democrat	Republican	Independent
Male	$ 10.5	$ 8.5	$ 12.5
Female	$ 13	$ 12	$ 14

The contract called for MAI to conduct interviews under the guidelines given below. Please help MAI to develop an interview plan.

Part 1. Linear Programming (LP) Model

Please formulate a linear programming (LP) model. Make sure you clearly define the decision variables, write the objective, and constraints. 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 5,000 total interviews.

At least 1,200 Independent voters must be interviewed.

At least 2,000 males must be interviewed.

At least 1,800 females must be interviewed.

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

No more than 30% of those interviewed may be Republicans.

No more than 20% 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.

Part 2. Spreadsheet Model and Solver Model

Construct a spreadsheet (Excel) modeland solve the problem by Excel Solver. Generate the Answer Report and Sensitivity Report from Excel Solver. Answer the following questions based on the Answer Report and Sensitivity Report from Excel Solver.

What is the optimal interview plan?

How much is the optimal total interview cost?

Related to contract requirement #3 given in Part 1:If the minimum number of males interviewed increases by 1 (i.e., changes from 2,000 to 2,001), how much will the total interview cost change (please indicate whether it is an increase, a decrease, or no change)?

Related to contract requirement #4 given in Part 1:If the minimum number of females interviewed increasesby 1 (i.e., changes from 1,800 to 1,801), how much will the total interview cost change (please indicate whether it is an increase,a decrease,orno change)?