Please answer the following:

4. (Output Maximization Problem): Suppose the production function is given by F(K, L) = 120KL, where K is the input of capital and L is the labour. Suppose prices of capital and labor are r = 2, and w = 5 respectively. The firm is given a budget of m dollars to spend on the two input factors. This translates to the following problem: mar120KL subject to 2K + 51 = m. (a) Find optimal choices of K and L as a function of m [5 marks]. (b) What is the additional increase in production, if m increases by 1 unit? [2 marks]