Chapter 2.5, Problem 300E

$\left[\text{T}\right]$ John allocates $d$ dollars to consume monthly three goods of prices $a,b,$ and $c.$ In this context, the budget equation is de?ned as $ax+by+cz=d,$ where $x\ge 0,y\ge 0,$ and $z\ge 0$ represent the number of items bought from each of the goods. The budget set is given by $\left\{\left(x,y,z\right)|ax+by+cz\le d,x\ge 0,y\ge 0,\right\},$ and the budget plane is the part of the plane of equation

$ax+by+cz=d$ for which $x\ge 0,y\ge 0,$ and $z\ge 0.$ Consider $a=\$8,b=\$5,c=\$10,$ and $d=\$500.$

1. Use a CAB to graph the budget set and budget plane.

For $z=25,$ find the new budget equation and graph the budget set ill the same system of coordinates.