A dietician wishes to mix two types of foods F_1 and F_2 in such a way that the vitamin content of the mixture contains at least 8 units of vitamin A…

A dietician wishes to mix two types of foods $\displaystyle \mathrm{F}_1$ and $\displaystyle \mathrm{F}_2$ in such a way that the vitamin content of the mixture contains at least $\displaystyle 8$ units of vitamin A and $\displaystyle 10$ units of vitamin C. Food $\displaystyle \mathrm{F}_1$ contains $\displaystyle 2$ units/kg of vitamin A and $\displaystyle 1$ unit/kg of vitamin C, while Food $\displaystyle \mathrm{F}_2$ contains $\displaystyle 1$ unit/kg of vitamin A and $\displaystyle 2$ units/kg of vitamin C. It costs ₹ $\displaystyle 5$ per kg to purchase Food $\displaystyle \mathrm{F}_1$ and ₹ $\displaystyle 7$ per kg to purchase Food $\displaystyle \mathrm{F}_2$.

Based on the above information, answer the following questions :

To find out the minimum cost of such a mixture, formulate the above problem as a LPP.

Determine the minimum cost of the mixture.