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 8 hours for each downhill and 6 hours for each cross-crountry ski. There are only 18 hours per week available for the manufacturing process and 64 hours for the finishing process. The average profit is $77 for downhill ski and $79 for cross-country ski. The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit.

Corner points of the feasible region:    
If there is more than one corner point, type the points separated by a comma (i.e. (1,2),(3,4)).

Maximum profit is: $  
when ____ downhill skis
and _____ cross-country skis are produced.

Answer 1

If downhill is produced,	Hours
Total finishing time available per week	64
Finishing time per downhill ski	8
Maximum number of skis can produce per week ( 64/8 ) = 8 skis
Therefore, maximum profit by producing maximum number of downhill skis per week = 8 skis x $ 77 = $ 616
If cross-country skis are produced,	Hours
Total manufacturing time available per week	18
manufacturing time per ski	2
Maximum number of skis can produce per week ( 18/2 ) = 9 skis
Therefore, maximum profit by producing maximum number of cross-country skis per week = 9 skis x $ 79 = $ 711
Conclusion; Company shall produce maximum number of corss-country skis by using maximum available manufacturing time available in a week.