CAT 1990 Question Paper Question 26

Instructions

A dealer deals only in colour TVs and VCRs. He wants to spend up to Rs.12 lakhs to buy 100 pieces. He can purchase a colour TV at Rs.10,000 and a VCR at Rs.15,000. He can sell a colour TV at Rs.12,000 and a VCR at Rs.17,500. His objective is to maximize profits. Assume that he can sell all the items that he stocks.

Question 26

For the maximum profit, the number of colour TVs and VCRs that he should respectively stock are

Solution

It is given that the maximum cost is 12 lakhs
$$1200000 <= T \times 10000 + V \times 15000$$ (Where T is number of TV's and V is number of VCR's)
and as we know $$T+V = 100$$
By solving the above two equation, we will get v<=40

We have to keep the no. of VCRs as maximum, as they fetch higher profit than TV, so

$$T = 60$$
$$V = 40$$

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