Problema Solution
A manufacturer of skis produces 2 types: downhill and cross country. Times for manufacturing each ski are given
Manufacturing each ski: Downhill 2.5 hours Cross Country 2 hrs
Finishing time per ski: Downhill 0.5 hours Cross Country 1.5 hours
The maximum total weekly hours available for manufacturing and finishing the skis are 70 hrs. and 36 hrs respectively. The profits per ski are $50 downhill and $70 cross country. Determine how many of each kind of ski should be produced to achieve a maximum profit.
Answer provided by our tutors
Let x be the number of downhill skis.
Let y be the number of cross-country skis.
2.5x + 2y <= 70The inequality for the manufacturing time of the skis.
.5x + 1.5y <= 36The inequality for the finishing time of the skis.
P = 50x + 70yThe profit function to be maximized.
Graphing the two inequalities (which can be done easily at www.desmos.com/calculator) gives a Feasible Region with intersections points at (0, 0), (0, 24), (28, 0), and (12, 20).
Plugging each of those points into the Profit functions yields profits of $0, $1680, $1400, and $2000, respectively.
To achieve the highest profit of $2000, the company should manufacture 12 downhill skis and 20 cross-country skis.