Suppose that the production function is given as a function of two inputs, Land K, where L is the quantity of labor and K is the quantity of capital, and expressed as below: Q=65L-4L- + 32K-2K2 The price of output is $10 per unit, the price of labor is $40 per unit, and the price of capital is $80 per unit (note, P = 10, w = 40 and r = 80). Answer the followings. a. Derive the equations for MPL and MPK. b. Identify the equation of equality for cost minimization in this given example. C. If 4 units of capital are hired, how many units of labor is to be hired to meet the condition of cost minimization? d. If 7 units of labor are hired, how many units of capital is to be hired to meet the condition of cost minimization