Potty Astaire makes fine clothing tor big and tall men. A few years ago Astaire

Question

Potty Astaire makes fine clothing tor big and tall men. A few years ago Astaire entered the sportswear market with the Sunset line of shorts pants, and shuts Management wants to make the amount of each product that will maximize profits. Each type of clothing is routed through two departments. A and B The relevant data for each product are as follows. Department A has 110 hours of capacity, department B has 120 hours of capacity and 90 yards of material are available Each shirt contributes $10 to profits and overhead each pair of shorts $13. and oath pair of pants $22 let X_1 = number of shirts produced X_2 = number of shorts produced. X_3 = number of pants produced. Specify the objective function and constraints for the problem. Objective function Maximize Z =

Explanation / Answer

LetX1 = number of shirts produced

X2=number of shorts produced

X3=number of pants produced

Here the objective function is to maximize the profits

Given Profit of shirt is $10, Profit of shorts = $13, Profit of pants = $22

Objective function Maximize Z = 10X1 + 13X2+ 22X3

constraints subject to

2X1 + 2X2+ 3X3 <=110 (Department A capacity time)

1X1 + 3X2+ 4X3 <=120 (Department B capacity time)

2X1 + 1X2+ 4X3 <=90(Material)

X1 , X2 , X3 >=0

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