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  • A company manufactures two types of cardigans : type A and type B. It costs Rs 360 to make type A cardigan and Rs 120 to make type B cardigan. The company can make at most 300 cardigans and spend at most Rs 72,000 a day. The number of cardigans of type

A company manufactures two types of cardigans : type A and type B. It costs Rs 360 to make type A cardigan and Rs 120 to make type B cardigan. The company can make at most 300 cardigans and spend at most Rs 72,000 a day. The number of cardigans of type B cannot exceed the number of cardigans of type A by more than 200. The company makes a profit of Rs 100 for each cardigan of type A and Rs 50 for every cardigan of type B.

Formulate this problem as a linear programming problem to maximize the profit to the company. Solve it graphically and find the maximum profit.

 

 

 

 
 
 
 
 

Answers (1)

Let the number of cardigans of type A and type B be x and y resp. 

To maximize : z=100x+50y in Rs

Subject to constraints :

x\geq 0,y\geq 0,x+y\leq 300

360x+120y\leq 72000\Rightarrow 3x+y\leq 600

y\leq x+200\Rightarrow y-x\leq 200

Corner points Value of z (in Rs)
O(0,0) 0
A(200,0) 20000
B(150,150) 22,500  (MAX VALUE)
D(50,250) 17500
D(0,200) 10000

Hence, no. of cardigans of type A is 150 and no. of cardigans of type B is 150. Also maximum profit is Rs 22500.

Posted by

Ravindra Pindel

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