Indian Institute of Foreign Trade 2017 Solved Paper

Question : 62 of 114

Marks: +1, -0

A Pharmaceutical company produces two chemicals X and Y, such that X consists of 5% salt A and 10% salt B and Y consists of 10% salt A and 6% salt B . For producing the chemicals X and Y, the company requires at least 7 gm of Salt A and at least 7 gm of Salt B. If chemical X costs Rs. 10.50 per gm and chemical Y costs Rs. 7.80 per gm, what is the minimum cost at which the company can meet the requirement by using a combination of both types of chemicals?

Rs. 810
Rs. 850
Rs.537
None

Validate

Solution:

Choice (A) Suppose the quantities of chemicals X and Y are 100x and 100y gms respectively, then quantities of salt A and salt B in these chemicals will be 5x + 10y and 10x + 6y.
Given that 5x + 10y ≥ 7 and 10x + 6y ≥ 7. Solving these in-equations we get,

x ≥ { 2 }/ { 5 }

and

y ≥ { 1 }/ { 2 }

Taking minimum values of x and y, quantities ofchemical X and Y can be calculated as 40g and 50 grespectively and total cost is

40×10.5 + 50×7.8 = 810.

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