ou have just been promoted as manager of "Los Picantones" in Calahorra (La Rioja). This firm processes some gourmet agricultural products like red peppers. In particular, the production function in this industry isq= 200 K^0.4 L^0.6 using two variable factors of production, capital K (number of machine-hours) and labor L (number of human-hours).

a)Try to solve the problem in general. First obtain the optimal values of K and Lexpressed in terms of the prices and the production q. Next find the expression for the TC(q)

b)If you are using 200 machines and 3000 people each hour. What should bethe optimal relation between the prices of the 2 inputs if you are producing efficiently? A ratio of 20 to 1, 10 to 1? Justify your answer.

c)If the price of capital is 120 per unit, and the price of labor is 12 per unit, obtain the total cost function ofa firm in this industry? And the average cost?

d)Show in a figure the isoquant curves. Calculate the MRTS at the input values of b).Comment and explain the result