List of top Applied Mathematics Questions on Linear Programming

Solve the following linear programming problem graphically:
Maximize $z = 50x + 30y$
Subject to:
$2x + y \leq 18$
$3x + 2y \leq 34$
$x \geq 0$, $y \geq 0$

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% phosphoric acid.
After testing the soil conditions, a farmer finds that he needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for his crop.
If $F_1$ costs ₹ 6 per kg and $F_2$ costs ₹ 5 per kg, how much of each type of fertilizer should be used so that the cost is minimum.
Formulate a linear programming problem.