Question

# Total revenue is in dollars and x is the number of units. Suppose that the total...

Total revenue is in dollars and x is the number of units.

Suppose that the total revenue function for a commodity is

R = 81x − 0.02x2.

(a) Find R(100).
\$

Tell what it represents.

The actual revenue of the 100th unit is this amount. The revenue decreases by about this amount when the number of units is increased from 100 to 101.     100 units produce this amount of revenue. 101 units produce this amount of revenue. The revenue increases by about this amount when the number of units is increased from 100 to 101.

(b) Find the marginal revenue function.
MR =

(c) Find the marginal revenue (in dollars per unit) at

x = 100.

\$ per unit

Tell what it predicts about the sale of the next unit and the next 3 units.

The sale of the next unit will ---Select---increasedecrease the revenue by about \$ . The sale of the next 3 units will ---Select---increasedecrease the revenue by about \$ .

(d) Find

R(101) − R(100).

\$

Explain what this value represents.

actual revenue from 100 units actual revenue from the 101st unit     actual revenue from 101 units actual revenue from the 100th unit marginal revenue at x = 100

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