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A diet of a stic person must contain atl...

A diet of a stic person must contain atleast 4000 unit of vitamins, 50 unit of proteins and 1400 calories. Two foods A and B are available at cos of Rs. 4 and Rs. 3 per unit respectively. If one unit of A contains 200 unit of vitamis, 1 unit of protein and 40 calories, while one unit of food B contains 100 unit of vitamins, 2 unit of protein and 40 calories. Formulate the problem, so that the diet be cheapest.

A

`200x+100yge400, x+2yge50`
`40x+40y ge1400, x ge0 and y ge0`
`O.Fz=4x+3y`

B

`400x+200yge100,x+2yge50`
`40x+40yge1400, x ge0 and y ge0`
`O.Fz=4x+3y`

C

`100x+200yge4000, x+2yge50,`
`40x+40y ge1400, x ge0 and y ge0`
`O.F z=4 x+3y`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A

Let z be the profit function and x and y denote the productivity of food A and B respectively. Then
`200x+100yge4000`
`x+2yge50`
`40x+40ge1400`
O.Fz=4x+3y, x ge 0 and y ge0`
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