A stereo manufacturer determines that in order to sell x units of a new stereo, the price per unit, in rupees, must be p(x)= 1000-x. The manufacturer also determines that the total cost of producing x units is given by C(x) = 3000+20x.

a) Find the total revenue R(x).

b) Find the total profit P(x).

c) How many units must the manufacturer produce and sell in order to maximise profit?

d) What is the maximum profit?

e) What price per unit must be charged in order to make this maximum profit?

a) Total Revenue, R(x):
Revenue is given by the price per unit multiplied by the number of units sold:

R(x)=x⋅p(x)=x(1000−x)R(x) = x \cdot p(x) = x(1000 - x) R(x)=1000x−x2R(x) = 1000x - x^2

b) Total Profit, P(x):
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