Question

luluapple makes popular clothing. a few years ago Lulu apple introduced a new line of shorts, pants, and shirts. Management wants to make the amount of each product so as to maximize profits. Each type of clothing is routed through two departments A and B. the relevant data are as follows: product: Shirts, 2 hours of processing time in department A, and 1 hour in department B, and 2 meters of material required. product: Shorts, 2 hours of processing time in department A and 3 hours in department B, 1 meter of material required Product: Pants, 3 hours of processing time in department A and 4 hours in department B, 4 meters of material required. Department A has 120 hours of capacity, department B has 160 hours of capacity, and 90 meters of materials are available. each shirt contributes $10 to profits; each pair of shorts, $10; and each pair of pants, $23. a. formulate the problem algebraically a linear programming model for this problem b. solve this problem using excel.

Answer 1

Solution :

Shirt : Processing :2A + B , Material = 2 meter, Profit =$10

Shorts : Processing :2A+ 3B , Material =1 meter, Profit = $10

Pants: Processing: 3A + 4B , Material = 4 meter , profit = $23

Let we are producing X units of shirts Y units of shorts and Z units of pants

Then equation for Processing A

2X+ 2Y + 3Z <=120

Then equation for Processing B

X+ 3Y + 4Z <=160

Equation for material

2X+ Y + 4Z <=90

Constraints

A<= 120

B<= 160

Material M<= 90

Our aim to maximize the profit by producing X units of shirts , Y units of shorts and Z units of Pants and we are getiing profits of $10, $10 and $23 respectively so

Z (Maximize)= 10X + 10Y + 23Z

So solving on excel

After adding all the equation and constraints for A, B and Material and clicking solve we get the following results

maximum profit Z = 1500.83

No of shirts produced X = 45

No of shorts produced Y = 53.33

No of pants produced Z = 22.5