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Question

A company manufactures two types of toys A and B. A toy of type A requires 5 minutes for cutting and 10 minutes for assembling. A toy of type B requires 8 minutes for cutting and 8 minutes for assembling. There are 3 hours available for cutting and 4 hours available for assembling the toy in a day. The profit is Rs.50 each on a toy of type A and Rs.60 each on a toy of type B. How many toys of each type should the company manufacture in a day to maximize the profit? Use linear programming to find the solution

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Solution

Toy A Toy B Time in a day
Cutting time5 min8 min180 min
Assembling time10 min8 min240 min
Profit5060
Assumed quantityxy

Profit function z=50x+60y

5x+8y=180
AB
x 036
y22.5 0
x0,y0
5x+8y180
10x+8y240 or 5x+4y120

5x+4y=120
C D
x 024
y 300

Corner pointz=50x+60y
At O(0,0) 0
At D(24,0)1200
At E(12,15)1500
At A(0,22.5)1350

Hence the maximum profit is Rs.1500 at E(12,15).

622846_596602_ans_7b3b6039889d416e978922cd0d2ee025.png

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