(a) There are two types of fertilizers F_1 and F_2. F_1 consists of 10% nitrogen and 6% phosphoric acid. F_2 consists of 5% nitrogen and 10%…

There are two types of fertilizers $\displaystyle \mathrm{F}_1$ and $\displaystyle \mathrm{F}_2$. $\displaystyle \mathrm{F}_1$ consists of $\displaystyle 10$% nitrogen and $\displaystyle 6$% phosphoric acid. $\displaystyle \mathrm{F}_2$ consists of $\displaystyle 5$% nitrogen and $\displaystyle 10$% phosphoric acid. After testing the soil conditions, a farmer finds that he needs atleast $\displaystyle 14$ kg of nitrogen and $\displaystyle 14$ kg of phosphoric acid for his crop. If $\displaystyle \mathrm{F}_1$ costs ₹ $\displaystyle 6$ per kg and $\displaystyle \mathrm{F}_2$ costs ₹ $\displaystyle 5$ per kg, how much of each type of fertilizer should be used so that the cost is minimum. Formulate a linear programming problem.

Solve the following linear programming problem graphically :

Maximise $\displaystyle \mathrm{z}=50 x+30 \mathrm{y}$

subject to $\displaystyle 2 x+\mathrm{y} \leq 18$

$\displaystyle 3 x+2 \mathrm{y} \leq 34$

$\displaystyle x, \mathrm{y} \geq 0$.