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A company manufactures two types of sweaters, type A and type B. It costs Rs. 360 to make one unit of type A and Rs. 120 to make a unit of type B. The company can make atmost 300 sweaters and can spend atmost Rs. 72000 a day. The number of sweaters of type A cannot exceed the number of type B by more than 100. The company makes a profit of Rs. 200 on each unit of type A but considering the difficulties of a common man the company charges a nominal profit of Rs. 20 on a unit of type B. Using LPP, solve the problem for maximum profit.

A company manufactures two types of sweaters, type A and type B. It costs Rs. 360
to make one unit of type A and Rs. 120 to make a unit of type B. The company can
make atmost 300 sweaters and can spend atmost Rs. 72000 a day. The number of
sweaters of type A cannot exceed the number of type B by more than 100. The
company makes a profit of Rs. 200 on each unit of type A but considering the difficulties of a common man the company charges a nominal profit of Rs. 20 on a
unit of type B. Using LPP, solve the problem for maximum profit.

Grade:upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago
Hello student,
let the company manufactures sweaters of type A = x, and that of type B = y. daily
LPP is to Maximise P = 200x + 20y
such that x+y\leq300
360 x + 120y\leq72000
x – y\leq100
x\geq0 y\geq0
240-1154_Capture3.PNG
Getting vertices of the feasible region as
A (100, 0), B (175, 75), C (150, 150) and D (0, 300)
Maximum profit at B
So Maximum Profit = 200 (175) + 20 (75)
= 35000 + 1500
= Rs. 36500
Thanks and Regards
Shaik Aasif
askIITians faculty

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