QUESTION ONE

Suppose that the demand equation for a monopolist operating in Nairobiis P= (1/12)x² - 10x + 300 and the cost function is C(x) = 50x + 100 where x is the production level

a) Given that the total revenue R (x) =xP and that the Total Profit realized P(x) = R(x) - C(x), determine the R(x) hence the P(x).

b) Using the result in (a) above determine the production level x that maximizes Profit and hence the maximum profit.

c)The marginal revenue function (MR) for a product is MR = 44 - 5q. The marginal cost is MC = 3q + 20, and the cost of producing 80 units is Ksh.11,400 where q are the number of units produced and sold.

i) Determine the total profit function P(q)

ii) Using the result in (i) above, and the profit or loss from selling 100 units of the product