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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 2000 per day if it produces only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. If company makes profit of Rs.3 and Rs.5 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 2000 per day if it produces only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. If company makes profit of Rs.3 and Rs.5 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

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Maximize (Z) = 3x1+5x2Subject to constraints x1+2x2≤2000,
x1+2x2≤1500, x2≤600 Non Negative Restrictions x1, x2≥0
Z is maximum at(1000,500) and the maximum value is 5500
Hence for maximun 1000 dolls of type A and 500 dolls of type B should be produced
Thanks and Regards
Shaik Aasif
askIITians faculty
Soumitra Chakraborty
26 Points
4 years ago

Let XA and XB be the quantity of doll A and B respectively.

Max.Z = 3XA + 5XB

Subject to,

XA + XB ≤ 1500 --------------(1)

Let total time per day = T, So, the time taken to produce one doll A = T/2000

Therefore, the time required to produce one doll B = 2T/2000

So, T*XA/2000 + 2T*XB/2000 ≤  T

or, XA + 2XB ≤ 2000 -------------(2)

XB ≤ 600 ------------(3)

XA, XB ≥ 0 ------------(4)

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