5. A firm produces widgets with production function: $q = 2\sqrt{KL}$. In the short run, the firm's
amount of capital is fixed at $K = 100$. The rental rate is $v = 1$ and the wage for L is $w = 4$.
(a) Find the firm's short-run total cost curve (SRTC), short-run average cost curve (SRAC),
and the short-run marginal cost (SMC) function.
(b) Graph the firm's SAC and SMC using the following levels of production: $q = 25$ and
$q = 100$.
(c) Find the firm's total cost curve as a function of $q$, $w$, $v$, and $K_1$.
(d) What level of K should be chosen to minimize total cost (note: K will be a function of
$q$, $w$, $v$)?
(e) Use the above results to calculate the long-run total cost of production.