A firm can manufacture a product according to the production function:Q=F(K,L)=K^(3/4) L^(1/4).a.Calculate the average product of labour, AP_L, when the level of capital is fixed at 81 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 256 units of labour? b.Find an expression for the marginal product of labour, MP_L, when the amount of capital is fixed at 81 units. Then, calculate the marginal product of labour for 16 and 81 units of labour. c.Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit and can hire labour at $50 per unit, how many units of labour should the firm hire in order to maximize profits?

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If the production function is Q = 30 + 22L + 30K, what's the most you can produce with 5 workers (L) and 7 unit of capital (K)? Enter as a value.

Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1 and the cost of a unit of capital is $3. The manager of this firm is interested in finding the following information: a)    Type of returns to scale and the marginal products of labor and capital. b)    The marginal rate of technical substitution of labor for capital. Graph the isoquant map. c)    The firm is currently producing 100 units of output. Find the optimal cost-minimizing quantities of labor and capital. Graphically illustrate this optimal solution using isoquants and isocost lines. What is the minimum total cost? d)    The manager now wants to know the K/L ratio to produce anyoutput level at the minimum total cost. Represent graphically the expansion path in the long run.