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 chemicals 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?
Explanation:
Let the total quantity of chemicals A and B be a and b respectively.
∴ Quantity of salt A required = (0.05a + 0.1b) and Quantity of salt B required = (0.1a + 0.06b)
Atleast 7 gms of each salt need to be present.
∴ 0.05a + 0.1b ≥ 7 and 0.1a + 0.06b ≥ 7
On solving, b ≥ 50 and a ≥ 40
Consider the minimum quantities required of A and B as cost is to be minimized.
∴ Minimum cost = (10.5)(40) + (7.8)(50)
= 420 + 390 = Rs. 810
Hence, option (a).
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