Question

A manufacturer of downhill and cross-country skis reports that manufacturing time is 1 hours and 2 hours, respectively, per ski and that finishing time is 7 hours for each downhill and 5 hours for each cross-crountry ski. There are only 16 hours per week available for the manufacturing process and 49 hours for the finishing process. The average profit is $64 for downhill ski and $89 for cross-country ski. The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit.

Answer 1

To maximize the weekly profit, we can use linear programming techniques to determine the optimal number of downhill and cross-country skis that should be made.

Step-by-step explanation:

To maximize the weekly profit, we need to determine the number of downhill and cross-country skis that should be made. Let's assume we make x downhill skis and y cross-country skis.

The manufacturing time for downhill skis is 1 hour per ski, so the total manufacturing time for downhill skis would be 1x hours. Similarly, the total manufacturing time for cross-country skis would be 2y hours. The finishing time for both types of skis is given as 7 hours for downhill skis and 5 hours for cross-country skis.

Considering the constraints, we have the following equations:

1x + 2y ≤ 16 (manufacturing time constraint)
7x + 5y ≤ 49 (finishing time constraint)
x, y ≥ 0 (non-negativity constraint)

The average profit for downhill skis is $64 and for cross-country skis is $89. So, the objective function is: Z = 64x + 89y (profit function)

To solve this problem, we can use linear programming techniques such as graphing, substitution, or elimination. The solution to this problem will provide the optimal number of downhill and cross-country skis that should be made to maximize the weekly profit.