Algebra

Consider the constraints

$2x+y6$

$y-x2$

$y+2x$

$x,y0$

$($a$)$ Plot the constraints and shade the feasible region.

In your plot, label each line which forms the boundary of the feasible region.

$($b$)$ Find all vertices of the feasible region.

Calculus

Consider the two functions $f,g$:$[-1,5]R,$ whose graphs are given below.

Calculate ${\displaystyle \underset{-1}{\overset{5}{}}}4f(x)-3g(x)dx.$

Explain all of the steps in your calculation.l