Question

also answer what is the maximum profit?

Question Help O 5.3.49-BE Amanufacturing company makes her types of water skin, a tricks and a slalom skl. The relevant manufacturing dat we given in the table Labor Hours per SM Maximum Labor-Hours Department Tricks Slalom SNI Available per Day Fabricating 243 Finishing Anwer parts (A and (A) the profit on a trick is $30 and the profit on a slalomski is $80, how many of each type of ski should be manufactured each day to realize ammum profit? What is the maximum profit? The mamum profitis The maximum occurs when trick skis and slalomskis are produced

Answer 1

The given information is Jabour hours per ski тах labour Per day Trick ski Slalom ski 9 6 243 Fabricating Finishing 36 and Now , Jet x be the no. of trick skis produced per day. be the no. of slalom skis produced per day. let Now, the inequality for fabricating and finishing hoill be: for fabricating : For finishing 9x + 6 Y S 243 .. xty < 36 and also X,Y 20 [as it cannot be negative] we Plotting these two inequalities graphically, get the feasibility region. CS Scanned with CamScanner

80 60 (0, 36) 40 (9, 27) 20 X+y=36 (27,0) 0 20 40 --20 9x+6y=243

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Now the constraints for the bounded region are 2 -0, y .36 u 29, y. 327 RE 27, y=0 Given that price of trick ski $ 30 per one price of slalom ski $ 60 per one Then the profit function n P30 + 604 From the graph we can see that maximum at X = 9, Y - 27. Therefore, pa 30x + 607 p. 30(9) + 60 (27) 2 270 + 8620 =$1890 the maximum profit of $ 1890 occurs at a trick skis and 27 slalom skis. CS Scanned with CamScanner

Therfore the maximum profits of $1890 occurs at 9 trick skis and 27 slalom skis.