Suppose a company can manufacture P(w,y) units of a certain product by utilizing a: units of labour and y units of capital. Furthermore, suppose the unit cost of labour and the unit cost of capital arep and qdollars respectively (p > 0, q > 0). Finally, suppose that the management of the company has allocated 0 dollars for the manufacture of the product. Do the following: (a) Use the method of Lagrange multipliers to show that at the maximum level of production 131(1'0790) : g P's/(960,90) q where :60 and go are the units of labour and capital, respectively, used at that level, and P1600, yo) and Py($o,yg) are not both zero. (b) Suppose that the output of the nished product is described by f(:z, y) : azl'yl'b. Find the amount of money to be spent on labour and capital to maximize the production