[Chapter 12] Linear Optimization Models Highland Marketing Group is a full-service marketing research company. Highland 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. The contract called for Highland to conduct interviews under the requirements (as detailed in the Constraints section) given below. Please help Highland develop an interview plan by formulating a linear optimization model. I. Define the decision variables. I. 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; X6= Number of voters who are Independents and from the Suburbs interviewed. II. Write the objective (mathematically). II. Write the objective (mathematically). Question 2 (2 points) What is the objective? MaxMinMinMinMaxMaxZ=x1+x2+x3+x4+x5+x6Z=18x1+16x2+22x3+21x4+20x5+25x6Z=x1+x2+x3+x4+x5+x6Z=18x1+21x2+16x3+20x4+22x5+25x6Z=18x1+21x2+16x3+20x4+22x5+25x6Z=18x1+16x2+22x3+21x4+20x5+25x6 III. Write the constraints (mathematically), which are the contract requirements. III. Write the constraints (mathematically), which are the contract requirements. Question 3 (3 points) At most 30% of the total voters interviewed may be Republicans and from the City. x20.3(x1+x2+x3)x20.3(x1+x2+x3)x20.3(x1+x2+x3+x4+x5+x6)x20.3x1+x2+x3+x4+x5+x6x20.3(x1+x2+x3+x4+x5+x6)x20.3x1+x2+x3+x4+x5+x6 At least 400 voters from the Suburbs must be interviewed. 21x4+20x5+25x640021x4+20x5+25x6400x4+x5+x6400x4+x5+x6400x4+x5+x6400x4+x5+x6=400 At least 1,200 voters must be interviewed. x1+x2+x3+x4+x5+x6>1,200x1+x2+x3+x4+x5+x61,20018x1+16x2+22x3+21x4+20x5+25x61,20018x1+16x2+22x3+21x4+20x5+25x61,200x1+x2+x3+x4+x5+x6=1,200x1+x2+x3+x4+x5+x61,200x1+x2+x3+x4+x5+x670018x1+16x2+22x3700 At most 50% of the total voters interviewed may be Democrats. x1+x40.5x1+x40.5x1+x40.5(x1+x2+x3+x4+x5+x6)x1+x40.5(x1+x2+x3+x4+x5+x6)x1+x40.5x1+x2+x3+x4+x5+x6x1+x40.5x1+x2+x3+x4+x5+x6x1+x4>0.5(x1+x2+x3+x4+x5+x6)x1+x40.4(X1+X2+X3+X4+X5+X6)X2+X50.4X1+X2+X3+X4+X5+X6X2+X50.4X1+X2+X3+X4+X5+X6X2+X50.2(x1+x2+x3+x4+x5+x6)x60.2(x4+x5+x6)x60.2x1+x2+x3+x4+x5+x6x60.2(x1+x2+x3+x4+x5+x6)x6300x3+x6=300x3+x60x1,x2,x3,x4,x5,x60x1+x2+x3+x4+x5+x60x1+x2+x3+x4+x5+x60x1,x2,x3,x4,x5,x6=0or1 IV. Construct an Excel Model and solve the optimization problem with Excel Solver. Answer the following questions based on the results from Excel Solver. Note: You are not required to submit your Excel Model. At the optimal solution, which statement is CORRECT about X1 (As previously defined, X1 is the number of voters who are Democrats and from the City interviewed)? 300600500$30,000$25,000