Question

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
(a) Find the daily total revenue realized from the sale of 230 units of the toaster oven.
(b) Find the additional revenue realized when the production (and sales) level is increased from 230 to 330 units.

Answer 1

Answer:

$1,200

Step-by-step explanation:

Data provided in the question:

R'(x)= -0.1x + 40

now,

Revenue function = ∫R'(x)= ∫(-0.1x + 40)

or

R(x) = $\frac{-0.1x^2}{2}+40x+c$

here, c is the integration constant

also,

at x = 0, Revenue R = 0

thus,

0 = $\frac{-0.1(0)^2}{2}+40(0)+c$

or

c = 0

therefore,

we get the revenue function as;

R(x) = $\frac{-0.1x^2}{2}+40x$

a) For x = 230 units

R(230) = $\frac{-0.1(230)^2}{2}+40(230)$

or

R(230) = - 2645 + 9200 = $6,555

b) R(330) =  $\frac{-0.1(330)^2}{2}+40(330)$

or

R(330) = -5445 + 13,200 = $7,755

Hence,

the addition evenue realized when the production (and sales) level is increased from 230 to 330 units

= $7,755 - $6,555

= $1,200