Question

At one of its factories, a manufacturer of college logo sweatshirts makes two styles: Crewneck pullover and hooded. Each pullover Sweatshirt takes 5 minutes to cut out and 20 minutes to assemble and finish. Each hooded sweatshirt takes 5 minutes to cut out and 30 minutes to assemble and finish. The plant has enough workers to provide at most 3,750 minutes per day for cutting and at most 19,500 minutes per day for assembly and finishing. The profit on each pullover Sweatshirt is $7 and the profit on each hooded sweatshirt is $9. How many of each sweatshirt should be produced each day to obtain maximum profit? Find the maximum daily profit pulover sweatshirts hooded sweatshirts prolit $

Answer 1

sembly of bo maximum Hm available solution. let unit of pullover Sweatshirts be made + os unit of hooded sweatshirt be made Time consumed in cutting of pull over sweat shirt bare SXX 5x minutes Time consumed in cutting of hooded sweatshist 5x y sy Time consumed in assembly of pull over sweatshirt x x 20 200 minutes Time consumed hooded sweatshirts 3oxy 3o y B Total time in cutting Sa+s4 Total time in am anembly and finish 20x + 30 y But it is given that for cutting 3750 U sat sy < 3750

and maximum time in assembly Igsoo 20 2030 + 30 y $ 19500 he have 5x+ sy s 3750 x + y 3750 ROM > aty < 45o 0 750 71750 o 2ont 3o y s 1950o 2x + 3y < 1950 19 SO 1 0 975 650 y 0 plotting both constraint we get 96 с feasible region bou so 400 300 200 x+y = 750 r I OD 200 300 You 0 (00 7) A E for we have 3 corner points (650,-) (0,750) 4 point B 1

for potut B x + y 7.50 --- ) 1950 2x + 3y = 07) 211) + 34 23/1 2x + 2y ISOD y 45o f x +450 = 750 7.30 - USD : 300 70 point B = (300 750) Now it given that profit in pullover Sweatshirt + 99 hooded - Sweatshirt profit in a total profit 7x + 9 g P 11 7x + ay we get butting (650,0) P = 2 X 650 + OX #USSO putting Co, 750) get 0X + 9 X 750 = $6750 putting (300 uso) we get 7 X 300 + 9x uso 6150 profit in maximum for (0,750)

pull over sweat shirt should be made A 750 hooded sweat shirt w should be made for maximum profit Pullover sweatshirts hooded 750 sweatshirt profit $ 6750