The total cost C for a manufacturer during a given time period is a function of the number N of items produced during thatperiod. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such asplant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find thetotal 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 thatperiod. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the totalrevenue, 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 manufacturerturns a profit, whereas if this number is negative, then the manufacturer has a loss. If the profit is zero, then themanufacturer is at a break-even point.In general, the highest price p per unit of an item at which a manufacturer can sell N items is not constant but is rather afunction 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 onN. The manufacturer has developed the following table showing the highest price p, in dollars, of a widget at which N widgetscan be sold.(a) Verify that the formula p = 50 - 0.04N, 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 ofwidgets soldp = Price100462004230040034500(b) Use the formula from part (a) and the fact that R is the product of p and N to find a formula expressing the totalrevenue R as a function of N for this widget manufacturer.R =(c) Express using functional notation the total revenue of this manufacturer if there are 375 widgets produced in amonth, and then calculate that value. (Round your answer to the nearest cent.)R(

Given the price function p=50-0.04N.

(a) Verify that the formula p = 50 - 0.04N, where p is the price in dollars, gives the same values as those in the tabl Use the formula to fill in the missing values for p. N = Number of widgets sold p = Price 100 46 200 42 300 400 34 500 (b) Use the formula from part (a) and the fact that R is the product of p and N to find a formula expressing the total revenue R as a function of N for this widget manufacturer. R = (c) Express using functional notation the total revenue of this manufacturer if there are 375 widgets produced in a month, and then calculate that value. (Round your answer to the nearest cent.) R(

(a) Verify that the formula p = 50 - 0.04N, where p is the price in dollars, gives the same values as those in the tabl Use the formula to fill in the missing values for p. N = Number of widgets sold p = Price 100 46 200 42 300 400 34 500 (b) Use the formula from part (a) and the fact that R is the product of p and N to find a formula expressing the total revenue R as a function of N for this widget manufacturer. R = (c) Express using functional notation the total revenue of this manufacturer if there are 375 widgets produced in a month, and then calculate that value. (Round your answer to the nearest cent.) R(

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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 N 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 - 0.04N, 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
p = Price
100
46
200
42
300
400
34
500
(b) Use the formula from part (a) and the fact that R is the product of p and N to find a formula expressing the total
revenue R as a function of N for this widget manufacturer.
R =
(c) Express using functional notation the total revenue of this manufacturer if there are 375 widgets produced in a
month, and then calculate that value. (Round your answer to the nearest cent.)
R(

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