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.
(a) Find the daily total revenue realized from the sale of 180 units of the toaster oven.
$ ?
(b) Find the additional revenue realized when the production (and sales) level is increased from 180 to 280 units.
$ ?
To find the daily total revenue realized from selling 180 units of the toaster oven, we need to calculate the total revenue function. The daily total revenue can be found by integrating the marginal revenue function.
(a) To find the daily total revenue when selling 180 units, we need to integrate the marginal revenue function R'(x) from 0 to 180:
R(x) = ∫R'(x) dx
Since R'(x) is measured in dollars per unit, integrating it with respect to x will give us the total revenue in dollars.
(b) To find the additional revenue realized when the production level is increased from 180 to 280 units, we can subtract the total revenue at 180 units from the total revenue at 280 units.
Let's calculate the daily total revenue for both parts:
(a) Daily total revenue from selling 180 units:
R(180) = ∫R'(x) dx from 0 to 180
(b) Additional revenue when production increases from 180 to 280 units:
R(280) - R(180) = ∫R'(x) dx from 0 to 280 - ∫R'(x) dx from 0 to 180
To find the exact values of R(180) and R(280), we need the specific form of the marginal revenue function R'(x). If you provide that information, we can proceed with the calculations.