Suppose a company can manufacture P(m,y) units of a certain product by utilizing 1: units of labour and 3/ 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 C 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 Pz(1o,yo) : E lat/(30,30) q where m0 and yo are the units of labour and capital, respectively, used at that level, and P1(a:0, yo) and Py(a:g,y0) are not both zero. (b) Suppose that the output of the nished product is described by f(a:, y) = ambylb. Find the amount of money to be spent on labour and capital to maximize the production