Production

Consider a company with a production function given by: y = x1/2 (1) where w > 0 is the factor cost of input, x, and y is output. The company operates in a competitive market and thus takes the price, p, for granted. Task 1.a) How can I set up the company's problem and solve it, and comment on how the result depends on p and w? Task 1.b) How can I illustrates the company's production function(x,y) diagram? (by hand or with a program of your choice) by using: 1. isoprofit lines to illustrate the optimal production selection for p/w = 1. Also do it for p/w = 1/2 and p/w = 2 2. Why does the company's optimal choice depend only on the relationship between p/w and not the two individually? In another market, the company sells another product and does not charge the price for granted, but instead faces a demand curve of: D(p) = A - ap, where A, a > 0. It has the same production function as equation (1) above Task 1.c) How to set up the company's problem and how to solve it? Task 1.d) Calculate p the and marginal costs of your two optima and show the relationship between the two. Interpret the relationship between the two