Can someone please help me with the problem C and find part

Can someone please help me with the problem C and find part (i) and (ii) Problem is found here http://imgur.com/jCYdum7

Please show the steps so I can better understand the problem :) Thanks.

Solution

Price = p(x) = 53.3 - 8 ln x

i) Revenue = R(x) = x* p(x)

R(x) =( 53.3 - 8ln x)*x

R(100) = ( 53.3 - 8 * ln 100) * 100 = {53.3 - (8*4.61)} * 100 = 16.459*100 = 1645. 9 Dollars

ii) Marginal revenue

R\'(x) = (53.3 - 8 ln x) - 8x/x =53.3 - 8 ln x - 8 = 45.3 - 8 ln x

R\'(100) = 45.3 - 8 ln 100 = 8.45 dollars