Find the additional revenue realized when the production (and sales) level is increased from 150 to 250 units.

Question

Marginal Revenue

 The management of Ditton Industries has determined that the daily marginal revenue function associated with selling x units of their deluxe toaster ovens is given by the following, where R'(x) is measured in dollars/unit.

R'(x)=-0.1x+40

Answer 1

Integrate R'(x) to get R(x):

R(x) = ∫ (-0.1x + 40) dx = -0.05x² + 40x + C

No revenue if no sales (x =0) so C = 0 and R(x) = -0.05x² + 40x

The answer to (a) is R(200). I'll let you do the arithmetic.

(b) This would be R(300) - R(200). You could use the general formula for R(x) obtained in part (a), or use

............................300

R(300) - R(200) = ∫ R'(x) dx

..........................200

You could use this integral, with lower limit 0 and upper limit 200, to answer part (a) but you would need to realize that R(0) = 0, as was required there too.