(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 Cost Per Interview Democrat Republican Independent City $18 $16 $22 Suburbs $21 $20 $27 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. questions. 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: X = Number of voters who are Independents and from the Suburbs interviewed. 11. Write the objective (mathematically). Question 2 (1 point) Sewed This is a problem o minimization maximization If the objective function is written as AX, +BX+CXy+D X4+ EXsFX where A, B, C, D, E, and Fare the coefficients for X1, X2, X3, X4, Xs, and X respectively, then A- > . 18 10 BE 16 > 22 21 EE 20 27 A/ Round the final answer (if it is not an integer) to the nearest integer III. Write the constraints (mathematically), which are the contract requirements. Question 4 (2 points) Seved At least 10% of the total voters interviewed must be independents and from the Suburbs X62 0.1 X1 + X2 + xy + X:+ Xs + X) X0.1X+ X2 + X3 X4 X5 + X) OX 0.151 X3 X3 X4 X5 + X6 Ca 2014 * X5 X6) 99. Question 5 (2 points) Saved At most 30% of the total voters interviewed may be Democrats. O X1 + X450.3 (X1 + X2 + X3+ X4+X5 + X2) X1 + X4 20.3 (X1 + X2 + X3 + X4 + Xs+X) OXI +X4 > 0,3 ( XX2 + X + Xa X5 X6 OX1 + X4 0.3 X1 + X2 X3 + X4+ Xs+X X: +X2 1,500 OX; + Xo = 1,500 OX3 + X6 > 1,500 22 X3 + 27X6 2 1,500 22 X3 + 27 X 5 1,500 Question 9 (2 points) Saved At most.20% of the total voters interviewed may be Republicans and from the city. X2 50.2 X1 + X2 + X3 * X * Xs X22021X1 + X2 + X) X2 1,800 OX+ X2 + X3 $ 1.800 Question 11 (2 points) Saved At least 4,500 voters must be interviewed, OX, X2+Xg+X+X5 + Xo $ 4.500 OX1 + X2 + X3 + X4+ X5 + X 4.500 18 X1 +16 X2 + 22 X3 +21 X4+20 X5 +27 X6 $ 4,500 18 X16Xy + 22 X3 +21 X4 + 20 X: + 27 Xo - 4,500 OX+Xz+ X. + X4+X5-Xo 4.500 FI Question 12 (2 points) Saved Constraints on decision variables. X1 + X2 +X3 + X4+ Xs +X620 OX.X2 , Xs. X = 0 OX, X2, X3, X4, X5, X 50 Ox+X + X + 4 +Xs + Xe