Suppose that there are $100$ identical firms in a perfectly competitive industry. Each firm has a short$-$run total cost function given by:

$C(q)=0\mathrm{.}2q^2+4q+10$

a$.$ 'Calculate a typical firm's short$-$run supply curve as a function of market price $(P).$

b$.$ Calculate the short$-$run industry $($market$)$ supply curve.