Question

A mantacturer of downhill and cioss-country skis reports that manulacturing time is 1 hours and 2 hours, respectively, per skd and that finishing time is 7 hours for each downht and 3 hours for esch cros3-crountry sti. There are only 16 hours per week avalable for the manufacturing process and 35 hours for the finishing process. The average profit is $59 for downhil sk and $78 for cross-country sk. The manulacturer wants to know how many of each type of sho should be made to maximize the weekly profit.

Comer points of the teasble region:____________________________- If there is more than one corner point, type the points separated by a comma (ie. 11,2,13,44. )
Maximum proft is: ______________________
when______________- downhill skis and _________________cross country skis are produced.

Answer 1

To maximize the weekly profit, the number of downhill and cross-country skis to be produced needs to be determined. Constraints include manufacturing and finishing time limits, while the objective function is to maximize profit. The problem can be solved using graphing or simplex method to find the corner points of the feasible region.

Step-by-step explanation:

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

Given that the manufacturing time for downhill skis is 1 hour and for cross-country skis is 2 hours per ski, and the finishing time is 7 hours for each downhill ski and 3 hours for each cross-country ski, we can set up the following constraints:

• 1x + 2y ≤ 16 (manufacturing time constraint)
• 7x + 3y ≤ 35 (finishing time constraint)

The profit per downhill ski is $59 and per cross-country ski is $78. Therefore, the objective function to maximize the profit is Z = 59x + 78y. We can solve this linear programming problem using graphing or simplex method to find the corner points of the feasible region and determine the maximum profit.