Cost and revenue functions for a certain chemical manufacturer are given in the following figure. Marginal revenue at 20 tons is about how much?
A)$100/ton
B)$320/ton
C)$5,200/ton
D)$4,500/ton

Question

Cost and revenue functions for a certain chemical manufacturer are given in the following figure. Marginal revenue at 20 tons is about how much? 
A)$100/ton 
B)$320/ton 
C)$5,200/ton 
D)$4,500/ton

Quizplus · Accepted Answer

Marginal revenue can be found by taking the derivative of the revenue function, which is the slope of the revenue curve. From the graph, we can see that at 20 tons, the revenue is about $6,400. At 30 tons, the revenue is about $8,800. 
So, the change in revenue when 10 tons of chemicals are produced is $8,800 - $6,400 = $2,400. 
Therefore, the marginal revenue at 20 tons is approximately $2,400/10 tons = $240/ton. 
However, we need to be careful because the revenue function is not linear, so the slope (or marginal revenue) is not constant. We can estimate the marginal revenue at 20 tons by finding the slope of the tangent line to the revenue curve at that point. From the graph, we can see that the tangent line at 20 tons has a slope of about $320/ton. Therefore, the best choice is B, $320/ton.

Cost and Revenue Functions for a Certain Chemical Manufacturer Are