Z00026. Suppose cost and revenue are given by
C(x) = 7x; R(x) = 9x − 0.01x2
where costs and revenue are in dollars and x is the quantity of the commodity measured in ounces.
a. Find the marginal cost, marginal revenue, and marginal profit functions.
| marginal cost | C’(x)= |
| marginal revenue | R’(x)= |
| marginal profit | P’(x)= |
b. Calculate the actual cost, revenue and profit to produce and sell the 10th ounce of the commodity. Then use the marginal functions approximate the cost, revenue and profit to produce and sell the 10th unit. Compare the results by filling in the blanks.
Using the marginal cost function, the approximate cost to produce the 10th ounce is __________ dollars.
Producing the 10th ounce of the commodity actually costs _________ dollars. So our approximation was ____________.
Using the marginal revenue function, the approximate revenue from the sale of the 10th ounce is ____________ dollars.
The actual revenue from the sale of the 10th ounce of the commodity is __________ dollars. So our approximation was ___________.
Using the marginal profit function, the approximate profit from the production and sale of the 10th unit is ____________ dollars.
The actual profit from the production and sale of the 10th ounce of the commodity is ____________ dollars. So our approximation was ____________.
