McRobert's TV Shop sells 400 sets per month, at a price of $600 per unit. Market research indicates that the shop can sell one additional set for each $1 it reduces the price. The total revenue (in dollars) is given by , where x is the number of additional sets beyond the original 400. What is the marginal revenue if 300 more units are sold?
A) 0$1,600
B) -$100
C) 0$400
D) -$400
E) 0$800

Question

McRobert's TV Shop sells 400 sets per month, at a price of $600 per unit. Market research indicates that the shop can sell one additional set for each $1 it reduces the price. The total revenue (in dollars) is given by  , where x is the number of additional sets beyond the original 400. What is the marginal revenue if 300 more units are sold? ​
A) 0$1,600 
B) ​-$100 
C) 0$400 
D) -$400 
E) 0$800

Quizplus · Accepted Answer

To find the marginal revenue, we need to take the derivative of the revenue function with respect to x:

R(x) = (400 + x)(600 - x)

R'(x) = 600 - 2x

When 300 more units are sold, x = 700. So, the marginal revenue is:

R'(700) = 600 - 2(700) = -$400

Therefore, the best choice is D, as it provides the correct value for the marginal revenue.

McRobert's TV Shop Sells 400 Sets Per Month, at a Price