Question

The marginal revenue from selling x items is 90-0.02 x. The revenue from the sale of the first 100 items is 8800 dollars. What is the revenue from the sale of the first 200 items?

Answer 1

The revenue from the sale of the first 200 items is $17,400.

Step-by-step explanation:

The marginal revenue (MR) represents the additional revenue generated from selling one additional unit. To find the total revenue, you integrate the marginal revenue function with respect to x.

The given marginal revenue function is MR = 90 - 0.02x.

To find the total revenue function, integrate the marginal revenue function:

R(x) = ∫ (90 - 0.02x),dx

R(x) = 90x - 0.01x^2 + C

Now, we know that the revenue from the sale of the first 100 items is $8800. So, plug in x = 100 and solve for C:

R(100) = 90(100) - 0.01(100)^2 + C = 8800

9000 - 100 + C = 8800

C = 8800 - 9000 + 100

C = -100

Now that we have the constant C, the total revenue function is:

R(x) = 90x - 0.01x^2 - 100

To find the revenue from the sale of the first 200 items x = 200, substitute x = 200 into the total revenue function:

R(200) = 90(200) - 0.01(200)^2 - 100

R(200) = 18000 - 400 - 100

R(200) = 17400

Therefore, the revenue from the sale of the first 200 items is $17,400.