Given:
Marginal revenue (in dollars per unit) for a month is
[tex]MR=-0.5x+400[/tex]
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.
[tex]TR=\int MR dx[/tex]
[tex]TR=\int (-0.5x+400) dx[/tex]
[tex]TR=-0.5\int x dx+400\int 1 dx[/tex]
[tex]TR=-0.5\times \dfrac{x^2}{2}+400x[/tex]
Now, substitute x=30 in the equation of Total Revenue (TR).
[tex]TR=-0.5\times \dfrac{30^2}{2}+400(30)[/tex]
[tex]TR=-0.5\times \dfrac{900}{2}+12000[/tex]
[tex]TR=-225+12000[/tex]
[tex]TR=11775[/tex]
Therefore, the total revenue from the production and sale of 30 units is $11,775.
