A small company makes custom surfboards. They have found that if they sell the surfboards for $100 thedemand is 100 boards. If they sell the surfboards for $80, the demand is 140 surfboards.a. Find a linear demand equation showing the number of surfboards, q, demanded as a function of theselling price p and then use the demand function to build the revenue function.b. If the marginal cost to produce each surfboard is $40 and there are fixed costs of $1000, report thecost and profit functions as a function of the price p.c. Determine what value ofpwill maximize profit? What is the maximum profit? How many surfboardsare sold at that price?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A small company makes custom surfboards. They have found that if they sell the surfboards for $100 the
demand is 100 boards. If they sell the surfboards for $80, the demand is 140 surfboards.
a. Find a linear demand equation showing the number of surfboards, q, demanded as a function of the
selling price p and then use the demand function to build the revenue function.
b. If the marginal cost to produce each surfboard is $40 and there are fixed costs of $1000, report the
cost and profit functions as a function of the price p.
c. Determine what value of
p
will maximize profit? What is the maximum profit? How many surfboards
are sold at that price?

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