Question

Ken Gilbert owns the Knoxville Warriors, a minor league baseball team in Tennessee. He wishes to move the Warriors south, to either Mobile (Alabama) or Jackson (Mississippi). The table below gives the factors that Ken thinks are important, their weights, and the scores for Mobile and Jackson.

Factor weight mobile jackson
Incentive 0.040 80 55
Player satisfaction 0.30 15 50
Sports interest 0.20 40 85
Size of city 0.10 75 30
a) Based on the given information, the best location for the Warriors to relocate to is, with a total weighted score of. (Enter your response rounded to two decimal places.) b) Jackson just raised its incentive package, and the new score is 75. Why doesn't this impact your decision in part (a)? A. Even if the score is 75, Jackson's total weighted score drops to 57, just ahead of Mobile. B. Because Jackson is already the better site. C. Even if the score is 75, Jackson will stay as the second choice.

Answer 1

Jackson has the higher total weighted score making it the better location for the Knoxville Warriors to relocate, and even with the increased incentive score, Jackson remains the best option.

Step-by-step explanation:

To answer the first question, we must calculate the total weighted score for both Mobile and Jackson using the given factors and their respective weights. Here is how the calculation is done:

• Incentive: Mobile (0.04 × 80) = 3.2, Jackson (0.04 × 55) = 2.2
• Player satisfaction: Mobile (0.30 × 15) = 4.5, Jackson (0.30 × 50) = 15
• Sports interest: Mobile (0.20 × 40) = 8, Jackson (0.20 × 85) = 17
• Size of city: Mobile (0.10 × 75) = 7.5, Jackson (0.10 × 30) = 3

Total Weighted Score for Mobile: 3.2 + 4.5 + 8 + 7.5 = 23.2

Total Weighted Score for Jackson: 2.2 + 15 + 17 + 3 = 37.2

Based on the total weighted scores, the best location for the Warriors to relocate to is Jackson with a total weighted score of 37.2.

For the second question, altering Jackson's incentive score to 75 would change its incentive weighted score to (0.04 × 75) = 3, but this still keeps the total weighted score for Jackson higher than Mobile's score. Therefore, even with the increased incentive score, our decision remains the same.

The adjusted claim B is correct in that Jackson is already the better site, even with the increased incentive score. It remains the first choice because the overall weighted score is still higher than Mobile's.

Answer 2

The best location for the Warriors to relocate to is Jackson, with a total weighted score of 37.2.

The best location for the Warriors to relocate to is still Jackson.

How to solve

The factors that Ken thinks are important and their weights are given in the table below:

Factor Weight

Incentive 0.040

Player satisfaction 0.30

Sports interest 0.20

Size of city 0.10

The scores for Mobile and Jackson are also given in the table below:

Factor Mobile Jackson

Incentive 80 55

Player satisfaction 15 50

Sports interest 40 85

Size of city 75 30

To calculate the total weighted score for each location, we multiply each score by its weight and add the products together. For Mobile, the total weighted score is:

(0.040 * 80) + (0.30 * 15) + (0.20 * 40) + (0.10 * 75) = 30.8

For Jackson, the total weighted score is:

(0.040 * 55) + (0.30 * 50) + (0.20 * 85) + (0.10 * 30) = 37.2

Therefore, the best location for the Warriors to relocate to is Jackson, with a total weighted score of 37.2.

Even with an increased score of 75 in the "Incentive" factor for Jackson, its higher-weighted factors compared to Mobile still make Jackson the better choice, as these factors have a greater influence on the overall decision.

Here is the calculation of the total weighted score for Jackson with the updated score for the "Incentive" factor:

(0.040 * 75) + (0.30 * 50) + (0.20 * 85) + (0.10 * 30) = 38.2

As you can see, Jackson's total weighted score is still higher than Mobile's total weighted score of 30.8. Therefore, the best location for the Warriors to relocate to is still Jackson.