For the Cobb$-$Douglas production function $P$ and isocost line $($budget constraint, in dollars$),$ find the amounts of labor $L$ and capital $K$ that maximize

production, and also find the maximum production. Then evaluate and give an interpretation for $||$ and use it to answer the question.

$($a$)$ Maximize $P=2000L^{\frac{3}{5}}{K}^{\frac{2}{5}}$ with budget constraint $15L+320K=8000.$

$L=$

$K=$

$P=$

$($b$)$ Evaluate and give an interpretation for $||.$

Each additional dollar of budget

production by this amount.

$($c$)$ Approximate the increase in production if the budget is increased by $$100.$

units