3 4 6 7 [Chapter 11] Linear Optimization Models Emerald Marketing Group is a full-service marketing research company. Emerald 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 the population. Based on previous studies, estimates of the interviewing costs for different types of voters are given in the table below. B 9 10 11 12 Cost Per Interview Democrat Republican Independent Page 3: City $18 $16 $22 13 14 15 Suburbs $21 $20 $27 16 17 18 The contract called for Emerald to conduct interviews under the requirements (as detailed in the Constraints section) given below. Please help Emerald develop an interview plan by formulating a linear optimization model. Write your final answer only (without intermediate steps) for the fill-in-the-blank questions. signment 2 ength: 1:00:00 Time Taken:0:02:56 Sandy Solayman: Attempt 1 3 1 6 7 9 10 1. Define the decision variables. (Note: This step is done for you. Please use these decision variables hereafter.) X1 = Number of voters who are Democrats and from the City interviewed; X2 = Number of voters who are Republicans and from the City interviewed; X3 = Number of voters who are independents and from the City interviewed; X4 = Number of voters who are Democrats and from the Suburbs interviewed: X5 = Number of voters who are Republicans and from the Suburbs interviewed: Xo = Number of voters who are independents and from the Suburbs interviewed. II. Write the objective (mathematically). Question 2 (1 point) This is a problem. 12 ge 3: 14 15 5 17 18 minimization maximization Assignment 2 Est. Length: 1:00:00 Time Taken:0:03:19 Sandy Solayman: Attempt 1 2 3 4 III. Write the constraints (mathematically), which are the contract requirements. Question 4 (2 points) At most 30% of the total voters interviewed may be Democrats. 5 6 7 8 9 10 OX+ X0.3 X1 + X2 + X3 + Xx+X5 + X6 X1 + X2 0.3 (X1 + X2 + X3 + Xx + X5 + X:) 11 12 X1 + X450.3 X1 + X2 + X3 + X4 + Xs + X) Page 3: 13 14 15 OX: +X>0.3 (X1 + X2 + X5 +X) X1 + X4 20.3 (X2 + x2 + x3 + X4 + X5 + X) 16 17 18 Question 5 12 points) At least 2,000 voters from the Suburbs must be interviewed. ARA