A diet is to contain at least 80 units of Vitamin A and 100 units of minerals. Two foods F1 andF2 are available. Food F1 costs Rs. 4 per unit and F2 costs Rs. 6 per unit. One unit of food F1contains 3 units of Vitamin A and 4 units of minerals. One unit of food F2 contains 6 units ofVitamin A and 3 units of minerals. Formulate this as a linear programming problem and findgraphically the minimum cost for diet that consists of mixture of these two foods and alsomeets the minimal nutritional requirements.
Let x units of food F1 and y units of food F2 is mixed
Cost of F1 = Rs 4 per unit
Cost of F2 = Rs 6 per unit
We have to minimize the food cost i.e.
Z = 4x + 6y
Also, F1 contains 3 units of vitamin and 4 units of minerals per unit, and F2 contains 6 units of vitamin and 3 units of minerals
Now, diet should contain 80 units of vitamin A
⇒ 3x + 6y ≥ 80
Also, diet should contain 100 units of minerals
⇒ 4x + 3y ≥ 100
And clearly, x ≥ 0, y ≥ 0
Now, let’s plot and find the area of solution.
Therefore, cost is minimized at 
He should take 24 units of F1 and 
units of F2
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