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 two things. The first is the manufacturer's fixed costs. This amount covers expenses such as plant maintenance and insurance, and it is the same no matter how many items are produced. The second thing we need to know is the cost for each unit produced, which is called the variable cost. 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. The profit P for a manufacturer is the total revenue minus the total cost. 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. Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. Number N Price p 250 32.50 300 32.00 350 31.50 400 31.00 (a) Find a formula for p in terms of N modeling the data in the table. p = (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month. R = Is R a linear function of N? YesNo (c) On the basis of the tables in this exercise and using cost, C = 30N + 700, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month. P = Is P a linear function of N? YesNo

Principles of Accounting Volume 2

19th Edition

ISBN:9781947172609

Author:OpenStax

Publisher:OpenStax

Chapter2: Building Blocks Of Managerial Accounting

Section: Chapter Questions

Problem 5EA: Rose Company has a relevant range of production between 10,000 and 25.000 units. The following cost...

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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 two things. The first is the manufacturer's fixed costs. This amount covers expenses such as plant maintenance and insurance, and it is the same no matter how many items are produced. The second thing we need to know is the cost for each unit produced, which is called the variable cost.

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. The profit P for a manufacturer is the total revenue minus the total cost. 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. Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.

Number N	Price p
250	32.50
300	32.00
350	31.50
400	31.00

(a) Find a formula for p in terms of N modeling the data in the table.
p =

(b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.
R =

Is R a linear function of N?

YesNo

(c) On the basis of the tables in this exercise and using cost, C = 30N + 700, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month.
P =

Is P a linear function of N?

YesNo

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