#### Answer

Equilibrium price: $\$ 41.25$, and
Equilibrium quantity: $62.5$ diet pills.

#### Work Step by Step

The supply and demand functions we found:
$S(q)=0.5q+10$
$D(q)=-0.5q+72.50$.
Equilibrium: $S(q)=D(q)$
Solving for q,
$0.5q+10=-0.5q+72.50\qquad/+0.5q-10$
$q=62.50$
The corresponding equilibrium price is S(q)...
$S(62.5)= 0.5(62.5) +10$
$=31.25+10$
$=41.25$
Equilibrium price is $\$ 41.25$, and
Equilibrium quantity is $62.5$ diet pills.