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4.2k views
in Linear Programming by (58.3k points)

A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below:

Food Vitamin A Vitamin B Vitamin C
x 1 2 3
y 2 2 1

One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet?

1 Answer

+1 vote
by (53.1k points)
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Best answer

Mininize 

Z = 16x +20y Subject to the constraints 

(i) x + 2y ≥ 10 

(ii) 2x + 2y ≥ 12 ⇒ x + y ≥ 6 

(iii) 3x + y ≥ 8 (iv) x ≥ 0; y ≥ 0

shaded region is the un bounded solution region 

A (0,8) Z = Rs 160 

B (1,5) Z = Rs 116 

C (2,4) Z = Rs 112 

D (10,0) Z = Rs 160 

The cost is minimised at C (2,4) Z = Rs 112 

2 kg of X and 4 kg of Y.

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