How to solve this LP problem graphically?

Question

Max Z = $10x + 15y$

s.t.

$x \ge 400$

$x + y \le 1000$

$0.7x - 0.3y \ge 0$

$x,y \ge 0$

The first two constraints I understand how to graph, but how do I do the third one? How do I graph this inequality?

Thanks in advance.

Answer 1

Just solve the inequality for y.

$0.7x-0.3y\geq 0$

Adding $0.3y$ on both sides

$0.7x\geq 0.3y$

Dividing the equation by $0.3$

$\frac{0.7}{0.3}x\geq y$

$\frac{7}{3}x\geq y$

The constraint alone looks like below