Question in description

Question

Find the daily total revenue realized from the sale of 150 units of the toaster oven.

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

Total Revenue is the integral of Marginal Revenue

TR = integral of MR

MR = R'(x) = -.1x + 40

R(x) = integral of R'(x) = (-.1/2)x^2 + 40x

R(150) = (-.05)(150)^2 + 40(150) = -7.5(150) +40(150 = 32.5(150) = 4875

Total Revenue= $4,875 daily if they sell 150

Maximum Revenue would be when they sell 400 daily.

R(400) = (-.05)(400)^2 + 40(400) = $8,000

but Maximum Profit would be when they set Marginal Revenue = Marginal Cost. Without the cost functions, you can't determine that.

The integral of R'(x) would seem to include a constant term, but why would there be any revenue when x=0?