A firm,using two inputs K and L to produce one product,whose production function is ,responds to a quantity demanded of 300 units,?the price of L is 6,while the price of K is 10,What is his optimal cost and how many units of L and K will he use?
Please prove that the marginal production (MP) curve will across the average production (AP) curve at AP’s maximum,(Provided that the production function is differentiable)
A firm produces one product using two inputs (K and L),if the production function of the firm is linearly homogeneous function,please prove the Clark-Wicksteed product-exhaustion theorem,Namely

A firm uses two inputs K and L to produce one product whose production function market is ,The market demand function for the product is P=20-Q,while the labor market is complete with wage w=4,In some period his capital K is fixed at 4 units and?,the price of K,is 10,
a) How many units of L should he use?
b) The product price P? The production Q and his profit.
Please prove that the short-run marginal cost (SMC) equal to the short-run average cost (SAC) at SAC’s minimum,(Provided that the total variable cost function is differentiable)