x=units sold, Find maximum profit and number of units that must be sold, in order to yield the maximum profit for each R(x)= 20x-0.1x^2, C(x)=4x+2

Revenue is given by the function:

R(x) = 20x - 0.1x^2

And cost of sales is given by the function:

C(x) = 4x + 2

Then profit will be given by the function:

P(x) = R(x) - C(x) = (20x - 0.1x^2) - (4x + 2)

P(x) = -0.1 x^2 + 16x - 2

To find the value of x where profit is maximum we differentiate P(x) and equate it to 0. Thus

- 0.2x + 16 = 0

0.2x = 16

x = 16/0.2 = 80

Profit when 80 unite are sold:

P(80) = -0.1*80^2 + 16*80 - 2 = - 640 + 1280 - 2 = 638

Answer:

Maximum profit is 638, which will be earned when 80 units are sold.