Suppose that the total cost of producing q widgets is given by C(q) = 0.02q + 50g + 1000. Also, suppose that the price of a widget is determined by p = %3D 100 – 0.005q. - а. What is the total revenue function? R(q) %3D b. What is the total profit function?

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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Suppose that the total cost of producing q widgets is given by
C(q) = 0.02q? + 50q + 1000. Also, suppose that the price of a
widget is determined by p = 100 – 0.005q.
a.
What is the total revenue function?
R(q)
b.
What is the total profit function?
T(q)
Graph the cost and revenue functions over a suitable interval on
the same set of axes. Sketch the graph below. Be sure to label
both curves. Indicate the region between the two curves that
represents a profit. Also, indicate the region(s) that represent a
loss. On a seperate set of axes, sketch the profit function on the
same interval. Indicate profit and loss on this graph. Write
interved
с.
interurds fur prutit ar loss in
notation.
How many widgets should the company sel(to maximize their
profit? What is the maximum profit? Label this point on the
profit graph.
d.
Widgets
Profit
Transcribed Image Text:Suppose that the total cost of producing q widgets is given by C(q) = 0.02q? + 50q + 1000. Also, suppose that the price of a widget is determined by p = 100 – 0.005q. a. What is the total revenue function? R(q) b. What is the total profit function? T(q) Graph the cost and revenue functions over a suitable interval on the same set of axes. Sketch the graph below. Be sure to label both curves. Indicate the region between the two curves that represents a profit. Also, indicate the region(s) that represent a loss. On a seperate set of axes, sketch the profit function on the same interval. Indicate profit and loss on this graph. Write interved с. interurds fur prutit ar loss in notation. How many widgets should the company sel(to maximize their profit? What is the maximum profit? Label this point on the profit graph. d. Widgets Profit
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