Question

A manufacturing company makes two types of water​ skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table.

	​Labor-Hours per Ski		Maximum​ Labor-Hours
Department	Trick Ski	Slalom Ski	Available per Day
Fabricating	55	44	140
Finishing	1	1	30

Answer parts​ (A), (B), and​ (C) below.

​(A) If the profit on a trick ski is ​$50 and the profit on a slalom ski is $30, how many of each type of ski should be manufactured each day to realize a maximum​ profit? What is the maximum​ profit? The maximum profit is ​$____. The maximum occurs when ___ trick skis and ___ slalom skis are produced.

Answer 1

Solution :- Given that, A manufacturing company makes two types of water skis, a Erick Ski and a slalom ski Let, Quantity of trick ski ST. Quantity of slalom ski es. profit = 50XT + 30%S, Subject to constraints :- 55 T +445 3140 T+S $30 + TSO sco from equation ① x H

+HT-+ + S = 1300 - 35 Equating the constraints, From $FO. We Met at WW1$ = 1320 557 + why s = 140 + ☺ - 0 -1 T T = 1180 --1180 T =-107127. Subtracting equation 0. 55(407, 27) +HH S = 140 -5899.85+445 =140 HHS = 1H0+5899.85 WHS 0 6039185 S = 6039.85 S =137,269

5 Maximize profit = 50X-107.27 +30X137,869. 5-6363,5+4118.07. = 124543. 2-1245-43 Maximize profit =$-1245,431 * Quantity of Trick ski = -107227. of slalom => Quantity Ski = 137, 269.