A dietician wishes to mix two types of foods in such a way that the vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C while Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs.5 per kg to purchase food I and Rs.7 per kg to purchase Food II. Determine the maximum cost of such a mixture. Formulate the above as a LPP and solve it graphically.

Suppose the dietician mixes x kg of food I and y kg of food II.
The first condition of the mixture containing 8 units of vitamin A is given by 2x + y ≥ 8
Also, at least 10 units of vitamin C is given by x + 2y ≥ 10
The total cost of the mixture is given by 5x + 7y
So, our problem becomes to maximize 5x + 7y, subject to the conditions
2x + y ≥ 8 .. (1)
and x + 2y ≥ 10 .. (2)
Equation (1) multiplied by 2 gives 4x + 2y ≥ 16
and when subtracted with equation (2), we get 3x ≥ 6 or x ≥ 2
When substituted in equation (1), we obtain y ≥ 4
The minimum cost of such a mixture thus becomes 10 + 28 = Rs.38.
However, the maximum cost can go up to infinity.

Formation of LPP
To Maximize: 5x + 7y
Constraints: 2x + y ≥ 8
x + 2y ≥ 10
x ≥ 0, y ≥ 0

Verifying values at corner points:
Corner Points (0,8) (2,4) (10,0)
Value of 5x + 7y 56 38 50
Minimum at (2,4), and It can attain infinity as its maximum value.