The marginal revenue from producing $x$ units of a certain product is
$100 + x - 0.001 x ^ { 2 } + 0.00003 x ^ { 3 }$ (in dollars per unit).
Find the increase in revenue if the production level is raised from 1,100 units to 1,700 units.
A) $\$ 51,366,000$
B) $\$ 51,367,000$
C) $\$ 17,765,250$
D) $\$ 26,866,667$
E) $\$ 37,974,583$

Question

Quizplus · Accepted Answer

The increase in revenue is the integral of the marginal revenue function from 1,100 to 1,700 units.$$\int_{1100}^{1700} (100 + x - 0.001 x ^ { 2 } + 0.00003 x ^ { 3 }) dx$$$$= [100x + \frac{x^2}{2} - \frac{0.001 x ^ { 3 }}{3} + \frac{0.00003 x ^ { 4 }}{4}]_{1100}^{1700}$$$$= 51,366,000$$

The Marginal Revenue from Producing xxx Units of a Certain Product Is

The Marginal Revenue from Producing $x$ Units of a Certain Product Is