The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced. The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative, then the manufacturer has a loss. If the profit is zero, then the manufacturer is at a break-even point. In general, the highest price p per unit of an item at which a manufacturer can sell W items is not constant but is rather a function of N. The total revenue R is still the product of p and N, but the formula for R is more complicated when p depends on N. The manufacturer has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. (a) Verify that the formula p = 50 -0.05N, where p is the price in dollars, gives the same values as those in the table. Use the formula to fill in the missing values for P. N = Number of widgets sold 100 200 R = 300 400 500 P = Price 45 40 30 (b) Use the formula from part (a) and the fact that R is the product of p and W to find a formula expressing the total revenue R as a function of N for this widget manufacturer. d (c) Express using functional notation the total revenue of this manufacturer if there are 475 widgets produced in a month, and then calculate that value. (Round your answer to the nearest cent.) R(475 ) = $d X
The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced. The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative, then the manufacturer has a loss. If the profit is zero, then the manufacturer is at a break-even point. In general, the highest price p per unit of an item at which a manufacturer can sell W items is not constant but is rather a function of N. The total revenue R is still the product of p and N, but the formula for R is more complicated when p depends on N. The manufacturer has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. (a) Verify that the formula p = 50 -0.05N, where p is the price in dollars, gives the same values as those in the table. Use the formula to fill in the missing values for P. N = Number of widgets sold 100 200 R = 300 400 500 P = Price 45 40 30 (b) Use the formula from part (a) and the fact that R is the product of p and W to find a formula expressing the total revenue R as a function of N for this widget manufacturer. d (c) Express using functional notation the total revenue of this manufacturer if there are 475 widgets produced in a month, and then calculate that value. (Round your answer to the nearest cent.) R(475 ) = $d X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
5
Expert Solution
Step 1
a)
for N = 300
p= 50 - 0.05 x 300 = 50 - 15 = 35
For N = 500
p = 50 - 0.05 x 500 = 50 - 25 = 25
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,