Question

If the marginal revenue (in dollars per unit) for a month is given by MR = −0.5x + 400, what is the total revenue from the production and sale of 30 units?

Answer 1

Given:

Marginal revenue (in dollars per unit) for a month is

$MR=-0.5x+400$

To find:

The total revenue from the production and sale of 30 units.

Solution:

We know that, total revenue is integration of marginal revenue with respect to quantity.

$TR=\int MR dx$

$TR=\int (-0.5x+400) dx$

$TR=-0.5\int x dx+400\int 1 dx$

$TR=-0.5\times \dfrac{x^2}{2}+400x$

Now, substitute x=30 in the equation of Total Revenue (TR).

$TR=-0.5\times \dfrac{30^2}{2}+400(30)$

$TR=-0.5\times \dfrac{900}{2}+12000$

$TR=-225+12000$

$TR=11775$

Therefore, the total revenue from the production and sale of 30 units is $11,775.