Question

In a mid-day meal programme, an NGO wants to provide vitamin rich diet to the students of an MCD school. The dietician of the NGO wishes to mix two types of food in such a way that vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food 1 contains 2 units per kg of vitamin A and 1 unit per kg of vitamin C. Food 2 contains 1 unit per kg of vitamin A and 2 units per kg of vitamin C. It costs Rs.50 per kg to purchase Food 1 and Rs.70 per kg to purchase Food 2. Formulate the problem as LLP and solve it graphically for the minimum cost of such a mixture.

Answer 1

Let x kg of Food 1 be mixed with y kg of Food 2.
To minimize Z= Rs. (50x+70y)

Subject to the constraints : $2x+y\ge 8,x+2y\ge 210,x\ge 0,y\ge 0$

$\begin{array}{cc}\text{Corner Points}& \text{Valu of Rs. (in Rs.)}\\ A(0,8)& 560\\ B(2,4)& 380\leftarrow \text{Min. value}\\ C(10,0)& 500\end{array}$

Since feasible region is unbounded so, 380 may or may not be minimum value of z.
To check, draw $50x+70y<380$ i.e., $5x+7y<38$.

As in the half plane $5x+7y<38$, there is no point common with the feasible region.

Hence minimum value of Z is Rs. 380.