You are a manager of a major manufacturer of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicate that the relevant production function is Q=2(K)^1/2 (L)^1/2, where K represents capital and L is labor. The rental rate for the capital is $1,000 per unit and the wage rate is $120 per labor. The market price for the chair is $400. From the production function, the marginal product of capital is MPK=(L/K)^1/2 and the product of labor is MPL=(K/L)^1/2. a. Suppose that in the short run, your company has spent $9,000 on 9 units of capital and this cannot be changed. What is your profit maximizing levels of labor input and the corresponding output and profit level? b. If the firm is free to choose any K and L, would the firm choose the Sam input as in part (a)? Explain