Question

Food X contains 6 units of vitamin A per gram & 7 units of vitamin B per gram and costs
5 per
gram. Food Y contains 8 units of vitamin A per gram & 12 units of vitamin B per gram and costs
7 per gram. The daily minimum requtement of vitamin A & B are 100 units and 120 units
respectively. The objective function i minimize cost is Min = =​

Answer 1

SOLUTION

GIVEN

• Food X contains 6 units of vitamin A per gram & 7 units of vitamin B per gram and costs 5 per gram.

• Food Y contains 8 units of vitamin A per gram & 12 units of vitamin B per gram and costs 7 per gram.

• The daily minimum requirement of vitamin A & B are 100 units and 120 units respectively.

TO DETERMINE

The objective function in minimize cost

EVALUATION

Let x gram of food X and y gram of food Y are required

Then

$\sf{x \geqslant 0 \: , \: y \geqslant 0}$

Now x gram of food X contains 6x units vitamin A and y gram of food Y contains 8y units of vitamin A

Now The daily minimum requirement of vitamin A is 100 units

$\sf{6x + 8y \geqslant 100}$

Now y gram of food Y contains 7x units vitamin A and y gram of food Y contains 12y units of vitamin B

Now The daily minimum requirement of vitamin B is 120 units

$\sf{7x + 8y \geqslant 120}$

Total cost = z = 5x + 7y

So the given linear programming problem can written as below

Minimize z = 5x + 7y

Subject to :

$\sf{6x + 8y \geqslant 100}$

$\sf{7x + 8y \geqslant 120}$

$\sf{x \geqslant 0 \: , \: y \geqslant 0}$

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