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A toy company manufactures two types of doll; a basic version-doll A and a deluxe version doll B. Each doll of type B takes twice as long as to produce as one of type A, and the company would have time to make a maximum of 3000 per day if it produces only the basic version. The supply of plastic is sufficient to produce 1800 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 900 per day available. If company makes profit of Rs.4 and Rs.3 per doll, respectively, on doll A and B; how many each should be produced per day in order to maximize profit.

A toy company manufactures two types of doll; a basic version-doll A and a deluxe version doll B. Each doll of type B takes twice as long as to produce as one of type A, and the company would have time to make a maximum of 3000 per day if it produces only the basic version. The supply of plastic is sufficient to produce 1800 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 900 per day available. If company makes profit of Rs.4 and Rs.3 per doll, respectively, on doll A and B; how many each should be produced per day in order to maximize profit.

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
Let x1, x2 be the number of dolls produced per day of type A and B
respectively. Let the doll A require ‘t’ hours so that the doll B requires 2t
hours.
Therefore, the total time to manufacture x1 and x2 dolls should not exceed
3,000t hours that is tx1 + 2tx2 ≤ 3000t
So. maximize Z=4x1+3x2
subject to constraints
x1+2x2≤3000
x1+x2≤1800
x2≤900
x1,x2>=0
so x1=x2=900
so Z=6300

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