(a)Suppose that a company's total cost function is:

TC = 100 + 50Q - 11Q²+ Q³

where,Qis the number of units of output produced.

i )At what level ofoutputwill the firm minimise its average variable cost AVC? What is thevalueof average variable cost at this output level?

ii)Discuss therelationshipbetween MC and marginal product (MP).Defineboth variables.

(b)i)Assume that the marginal product is decreasing. Can you determine whether the average product is increasing or decreasing?Explain.

ii)Explain the concept of marginal rate of technical substitution (MRTS).Suppose that a production process has a marginal rate of technical substitution,MRTS_L,K,of 2. The wage rate (w)is $4 and the rental rate of capital (r) is $2.What should the firm do in order to minimise cost.Explain.