A firm’s revenue (in thousand rupees) from selling x hundred units of a product is modelled by
R(x)=(x2+2x+1)(50−2x),0≤x≤25.
(a) Obtain the marginal revenue function R′(x).
(b) Determine the value of x that maximises the revenue.
(c) Calculate the maximum possible revenue (in thousand rupees) the firm can earn.
(d) Verify that the value of x found in part (b) indeed gives a maximum by examining the nature of R′(x) on either side of the point.