A supply function and a demand function are given.

Supply:

p $=1/5$q$^2+12$

Demand:

p $=976$q $2$q$^2$

$($a$)$ Sketch the first$-$quadrant portions of those functions on the same set of axes. Label the market equilibrium point E$.$

$($b$)$ Algebraically determine the market equilibrium point.

$($q$,$ p$)=($i$)$

$($i$)0$

$($i$)$

$($i$)$