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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. Cost Per Interview Democrat | Republican | Independent City Democrat $18. City Republican $16 | City Independent $22 Suburbs Democrat :$21 | Suburbs Republican $20 | Suburbs Independent $25 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. 1. Define the decision variables. (Note: This step is done for you. Please use these decision variables hereafter) X, = Number of voters who are Democrats and from the City interviewed; X= Number of voters who are Republicans and from the City interviewed; X; = Number of voters who are Independents and from the City interviewed; X= Number of voters who are Democrats and from the Suburbs interviewed; Xs = Number of voters who are Republicans and from the Suburbs interviewed; Xs = Number of voters who are Independents and from the Suburbs interviewed. 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. Question 12 At the optimal solution, which statement is CORRECT about X, (As previously defined, X; is the number of voters who are Democrats and from the City interviewed)? a. 100

Question:

Uploaded ImageHighland 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. Cost Per Interview Democrat | Republican | Independent City Democrat $18. City Republican $16 | City Independent $22 Suburbs Democrat :$21 | Suburbs Republican $20 | Suburbs Independent $25 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. 1. Define the decision variables. (Note: This step is done for you. Please use these decision variables hereafter) X, = Number of voters who are Democrats and from the City interviewed; X= Number of voters who are Republicans and from the City interviewed; X; = Number of voters who are Independents and from the City interviewed; X= Number of voters who are Democrats and from the Suburbs interviewed; Xs = Number of voters who are Republicans and from the Suburbs interviewed; Xs = Number of voters who are Independents and from the Suburbs interviewed. 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. Question 12 At the optimal solution, which statement is CORRECT about X, (As previously defined, X; is the number of voters who are Democrats and from the City interviewed)? a. 100

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Asked by: Test User 100161
Created at: 2025-05-06 12:04:08

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Let's break down the information and what is being asked: ### Information Provided #### Cost Per Interview - **City Democrat:** $18 - **City Republican:** $16 - **City Independent:** $22 - **Suburbs Democrat:** $21 - **Suburbs Republican:** $20 - **Suburbs Independent:** $25 #### Decision Variables - \( X_1 \): Number of City Democrats interviewed - \( X_2 \): Number of City Republicans interviewed - \( X_3 \): Number of City Independents interviewed - \( X_4 \): Number of Suburbs Democrats interviewed - \( X_5 \): Number of Suburbs Republicans interviewed - \( X_6 \): Number of Suburbs Independents interviewed --- ## Questions ### Question 12 > At the optimal solution, which statement is CORRECT about \( X_1 \) (number of City Democrats interviewed)? - a. 100 < \( X_1 \) ≤ 200 - b. 200 < \( X_1 \) ≤ 300 - c. 500 < \( X_1 \) ≤ 600 - d. 400 < \( X_1 \) ≤ 500 - e. \( X_1 \) > 600 - f. \( X_1 \) ≤ 100 - g. 300 < \( X_1 \) ≤ 400 ### Question 13 > Which statement is CORRECT about the optimal objective function value Z? - a. $25,000 < Z ≤ $30,000 - b. Z > $30,000 - c. $20,000 < Z ≤ $25,000 - d. $10,000 < Z ≤ $15,000 - e. $15,000 < Z ≤ $20,000 - f. Z ≤ $10,000 --- ## **How to Approach** Since the problem asks for the answers **based on results from Excel Solver** (which is not shown in the image), you must use the results you got from solving the model in Excel. However, if you do not have those results, *the answers cannot be determined precisely without running the model in Excel Solver*, as the values of \(X_1\) and \(Z\) depend on the constraints (not provided in the image). ### **How to Solve in General:** 1. **Formulate the Objective:** \[ \text{Minimize } Z = 18X_1 + 16X_2 + 22X_3 + 21X_4 + 20X_5 + 25X_6 \] 2. **Add the Constraints:** (These are not given in the image, but would typically include minimums/maximums for each category.) 3. **Run Solver in Excel:** Obtain the optimal values for \(X_1\) and \(Z\). --- ## **What to Do Next:** - If you have already run Excel Solver as instructed in the assignment, check your Solver results for: - The value of \(X_1\) (for Q12) - The value of \(Z\) (for Q13) - Match your results to the correct interval in each multiple choice. --- ### **If You Need to Guess:** - If you do not have Solver results, the correct answers cannot be determined. They are unique to the scenario, constraints, and solution found in Solver. --- **In summary:** - Use your Excel Solver output to answer Questions 12 and 13. - If you give me your Solver values for \(X_1\) and \(Z\), I can help you pick the right answers! - If you need help setting up the Excel Solver model, let me know!

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