Fairland Marketing Group is a full-service marketing research company. Fairland 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, estimates of the interviewing costs for different types of voters are given in the table below. 7 Cost Per Interview Democrat Republican Independent Male $20 $18 $24 Female $23 $22 $28 The contract called for Fairland to conduct interviews under the requirements (as detailed in the Constraints section) given below. Please help Fairland develop an interview plan by formulating an linear optimization model. Follow the steps below. 1. Define the decision variables. 10 (Note: This step is done for you. Please use these decision variables hereafter.) X1 = Number of Male Democrats interviewed; 15 X2 = Number of Male Republicans interviewed; 18 X = Number of Male Independents interviewed; X4 = Number of Female Democrats interviewed; Xs - Number of Female Republicans interviewed; Xo = Number of Female Independents interviewed. II. Write the objective (mathematically). Question 2 (2 points) Saved This is a problem. 4 minimization maximization 7 10 Question 3 (2 points) Saved The objective function is X1 + X2 + X3 + X4+ X5 + X6 20 X1 + 18 X2 + 24 X3 + 23 X4+ 22 X5 +28 X6 15 20 X1 + 23 X2 + 18 X3 + 22 X4 + 24 X5 + 28 X6 III. Write the constraints (mathematically), which are the contract requirements. Question 4 (2 points) Saved There should be at least 2,000 total interviews. X1 + X2 + X3 + X4 + X5 + X6 s 2,000 20 X1 + 18 X2 + 24 X3 + 23 X4 + 22 X5 + 28 X6 $ 2,000 X1 + X2 + X3 + X4 + X5 + X6 2 2,000 20 X1 + 18 X2 + 24 X3 + 23 X4 + 22 Xs + 28 X6 > 2,000 Question 5 (2 points) Saved At least 600 Independent voters must be interviewed. 5 OX3 + X6 2 600 3 24 X3 + 28 X6 2 600 24 X3 +28 Xo s 600 X3 + X6 s 600 Question 6 (2 points) Saved At most 30% of the total voters interviewed may be Democrats. X1 + X4 20.3 (X1 + X2 + X3 + X4 + X5 + X6) 4 X1 + X2 2 0.3 (X1 + X2 + X3 + X4 + X5 + X6) X1 + X2 3 0.3 (X1 + X2 + X3 + X4 + X5 + X6) 7 X1 + X4 S 0.3 (X1 + X2 + X3 + X4 + X5 + X6) 10 Question 7 (2 points) Saved At least 800 female voters must be interviewed. OX + Xs + X6 2 800 15 O 23 X4 + 22 Xs + 28 X6 > 800 18 23 X4 +22 X5 + 28 X6 800 OX + Xs + X6 x 800 Question 8 (2 points) Saved At most 40% of the total interviewed may be Republicans. X2 + X5 s 0.4 (X1 + X2 + X3 + X4 + X5 + X6) 4 OX2 + X5 0.4 X1 + X2 + X3 + X4 + X5 + X6 X2 + X5 30.4 7 X2 + X5 20.4 (X1 + X2 + X3 + X4 + X5 + X) 10 Question 9 (2 points) Saved At least 700 male voters must be interviewed. X1 + X2 + X3 $ 700 15 20 X1 + 18 X2 + 24 X3 2 700 18 20 X1 +18 X2 + 24 X3 $ 700 X1 + X2 + X3 2 700 Question 10 (2 points) At least 10% of the female voters interviewed must be independents. OXo
