Question

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 units/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 minimum cost of such a mixture. Formulate the above as a LPP and solve it graphically.

Answer 1

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

It z be the total cost of purchasing x kg of Food I and y kg of Food II then
z = 5x + 7y ...(v)
Here we have to minimise z subject to the constraints (i) to (iv)
On plotting inequalities (i) to (iv) we get shaded region having corner points A, B, C which is required feasible region.
Now we evaluate z at the corner points A (0, 8), B (2, 4) and C (10, 0)

Since feasible region is unbounded. Therefore we have to draw the graph of the inequality.
5x + 7y < 38 ...(vi)
Since the graph of inequality (vi) is that open half plane which does not have any point common with the feasible region.

So the minimum value of z is 38 at (2, 4).
i.e., the minimum cost of food mixture is Rs.38 when 2kg of Food I and 4 kg of Food II are mixed.