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If C(x) = 16,000 + 500x 1.6x² + 0.004x³ is the cost function and R(x) = 1700x - 7x² is the revenue function, find the production level that will maximize profit.

If C(x) = 16,000 + 500x 1.6x² + 0.004x³ is the cost function and R(x) = 1700x - 7x² is the revenue function, find the production level that will maximize profit.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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cost function and R(x) (b) If C(x) = 16,000 + 500x - 1.6x² + 0.004x³ is the 1700x 7x2 is the revenue function, find the production level that will maximize profit. = 21. Sustainable harvesting Example 5 was based on the assumption that we want to maximize the total harvest size H, but instead we might want to maximize profit. (a) Suppose the selling price of a unit of harvest is p dollars. and the cost per unit harvested is C dollars. (Assume p>C.) Show that the fishing effort that maximizes profit is the same as the effort that maximizes the har- vest size H. (b) Suppose the selling price of a unit of harvest is p dollars and the unit cost is inversely proportional to the fishing effort h (that is, C = a/h). Assume a < rp. What is the fishing effort that maximizes profit? What is the limiting population size, assuming this fishing effort is used?
Transcribed Image Text:cost function and R(x) (b) If C(x) = 16,000 + 500x - 1.6x² + 0.004x³ is the 1700x 7x2 is the revenue function, find the production level that will maximize profit. = 21. Sustainable harvesting Example 5 was based on the assumption that we want to maximize the total harvest size H, but instead we might want to maximize profit. (a) Suppose the selling price of a unit of harvest is p dollars. and the cost per unit harvested is C dollars. (Assume p>C.) Show that the fishing effort that maximizes profit is the same as the effort that maximizes the har- vest size H. (b) Suppose the selling price of a unit of harvest is p dollars and the unit cost is inversely proportional to the fishing effort h (that is, C = a/h). Assume a < rp. What is the fishing effort that maximizes profit? What is the limiting population size, assuming this fishing effort is used?
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no, please do question 21! a and b, not the one above it

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