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ufactu of Widg month, nable cost IS S60 per widget (So It costs $60 to produce 1 widget). Let N be the number of widgets produced in a month. (a) Find a formula for the manufacturer's total cost C as a function of N. C = (b) The manufacturer sells the widgets for $75 each. Find a formula for the total revenue R as a function of N. R = (c) Use your answers to parts (a) and (b) to find a formula for the profit P of this manufacturer as a function of N. P = (d) Use your formula from part (c) to determine the break-even point for this manufacturer. widgets/mo

ufactu of Widg month, nable cost IS S60 per widget (So It costs $60 to produce 1 widget). Let N be the number of widgets produced in a month. (a) Find a formula for the manufacturer's total cost C as a function of N. C = (b) The manufacturer sells the widgets for $75 each. Find a formula for the total revenue R as a function of N. R = (c) Use your answers to parts (a) and (b) to find a formula for the profit P of this manufacturer as a function of N. P = (d) Use your formula from part (c) to determine the break-even point for this manufacturer. widgets/mo

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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 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. A manufacturer of widgets has fixed costs of $180 per month, and the variable cost is $60 per widget (so it costs $60 to produce 1 widget). Let N be the number of widgets produced in a month. (a) Find a formula for the manufacturer's total cost C as a function of N. C = (b) The manufacturer sells the widgets for $75 each. Find a formula for the total revenue R as a function of N. R = (c) Use your answers to parts (a) and (b) to find a formula for the profit P of this manufacturer as a function of N. P = (d) Use your formula from part (c) to determine the break-even point for this manufacturer. |widgets/mo
Transcribed Image Text: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. A manufacturer of widgets has fixed costs of $180 per month, and the variable cost is $60 per widget (so it costs $60 to produce 1 widget). Let N be the number of widgets produced in a month. (a) Find a formula for the manufacturer's total cost C as a function of N. C = (b) The manufacturer sells the widgets for $75 each. Find a formula for the total revenue R as a function of N. R = (c) Use your answers to parts (a) and (b) to find a formula for the profit P of this manufacturer as a function of N. P = (d) Use your formula from part (c) to determine the break-even point for this manufacturer. |widgets/mo
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