Question #37a3d

1 Answer
Oct 10, 2017

x=8 and y=8 maximizes z so z=40

Explanation:

I’m going to use desmos.com to show what is going on, but you could do this by hand on graph paper as well:

Change the first two constraints so that they are inequalities of lines in slope intercept form:

x+y>10
y> -x+10 (above but not equal to the line y=-x+10)

x-y>0
y< x (below but not equal to the line y=x)

We know the other constraints keeps us between 0 and 8 on the x-axis, while also not letting us go below 0 on the y-axis.

So this is what the graph looks like on Desmos:enter image source here

We can see the region we care about is the triangle that is contained in the first quadrant. This region has 3 vertices that could maximize our function z.

Let’s try each point with the function z:

(8,8):2(8)+3(8)=40

(5,5):2(5)+3(5)=25

(8,2):2(8)+3(2)=22

Thus the point (8,8) maximizes z so x=8 and y=8