A firm sells a product for $80 per unit. Raw material costs are $12,50 per unit, labor costs are $27,50 per unit, and annual fixed costs are $260,000. a. Determine the profit function P(x), where x equals the number of units sold. b. How many units would have to be sold to earn an annual profit of $250,000.

A firm sells a product for $80 per unit. Raw material costs are $12,50 per unit, labor costs are $27,50 per unit, and annual fixed costs are $260,000. a. Determine the profit function P(x), where x equals the number of units sold. b. How many units would have to be sold to earn an annual profit of $250,000.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Elizabeth won $6,000 in the lottery. She started to spend it right away. After 4 weeks she had…

A: Explanation: Total money from lottery = $6000 Spen money in 4 weeks = $2200 Calculate the money…

Q: Suppose that a computer software company produces and sells a new operating system at a cost of $55…

A: The cost of new operating system is $55 per copy The fixed cost is $15,000 per month. If the number…

Q: An electric company charges $12.75 per month plus $0.49 per kilowatt-hour (kWh) for the first 200…

A: Fixed cost, F=$12.75 per month.Variable cost for first 200kWh, V1=$0.49 per kWh.Variable cost for…

Q: A two-day environmental clean up started at 9AM on the first day. The number of workers fluctuated…

Q: The total cost C for a manufacturer during a given time period is a function of the number N of…

Q: 9. Starbucks noticed that when they charged $2.50 for a cup of coffee, they sold 230,000 Ibs of…

A: Given C(x) = Coffee (in pounds ) sold. x = price per cup And…

Q: An author can typically expect to receive the following royalties on a published work in hardback…

Q: (a) Verify that the formula p = 50 - 0.04N, where p is the price in dollars, gives the same values…

A: Given the price function p=50-0.04N.

Q: Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed…

Q: The total cost C for a manufacturer during a given time period is a function of the number N of…

A: Given that the total cost can be calculated as the sum of fixed cost and the product of the variable…

Q: he total cost C for a manufacturer during a given time period is a function of the number N of items…

A: Given that: suppose that a manufacturer of vidgets has fixed costs of $5000 per month and that the…

Q: Assume that the situation can be expressed as a linear cost function. Find the cost function in this…

Q: A farmer can sell his potatoes for $8 per bushel today, but this price is dropping by 5¢ per day.…

Q: Suppose that a manufacturer of widgets has fixed costs of $9000 per month and that the variable cost…

Q: Suppose the supply per week for a product is 1254 units if the price per unit is $46 and 1518 units…

A: number of units/week supplied = 1254 price per unit $46 price per unit of 1518 units = 79$

Q: Drug C and Drug R are two different brands of a drug used to treat a disorder. a. Use the fact that…

A: Given that: For Drug C: y=2.9, x=0 and y=10.7,x=10. For Drug R: y=8, x=0 and y=5.2,x=10. To find…

Q: The manufacturer has developed the following table showing the highest price p, in dollars, of a…

A: Given : The formula p = 50 − 0.04 N, where p is the price in dollars . To determine : (a) Use the…

Question

A firm sells a product for $80 per unit. Raw material costs are
$12,50 per unit, labor costs are $27,50 per unit, and annual fixed
costs are $260,000.
a. Determine the profit function P(x), where x equals the number
of units sold.
b. How many units would have to be sold to earn an annual
profit of $250,000.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

You sell candy at an event to make money. When candy are sold for $1.10 per bag, approximately 625 bags are sold at each event. You tried to raise the price to $1.35 and found that the quantity demanded dropped to 525 bags. The startup cost was $500 and the cost to you per bag of peanuts is $0.50. Assume that the demand function is linear and write a function that models the profit from selling x bags of peanuts at an event. What number of bags and what price per bag will get you a maximum profit?
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.Suppose that a manufacturer of widgets has fixed costs of $7000 per month and that the variable cost is $16 per widget (so it costs $16 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.)C = (b) Express using functional notation the total cost if there are 225 widgets produced in a month.C( )Calculate the total cost if there are 225…
A company is planning to manufacture mountain bikes. Fixed monthly cost will be $300,000 and it will cost $200 to produce each bicycle. A. Write the cost function, C, of producing x mountain bikes. C(x) = per month B. Write the average cost function, C, of producing x mountain bikes. C(x) = per month %3D C. How many mountain bikes must be produced each month for the company to have an average cost of $300 per bike? must be produced each month. Enter your answer in each of the answer boxes.
A company produces very unusual CD's for which the variable cost is $ 11 per CD and the fixed costs are $ 35000. They will sell the CD's for $ 55 each. Let a be the number of CD's produced. Write the total cost C as a function of the number of CD's produced. C = $ Write the total revenue R as a function of the number of CD's produced. R= $ Write the total profit P as a function of the number of CD's produced. P = $ Find the number of CD's which must be produced to break even. The number of CD's which must be produced to break even is
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.Suppose that a manufacturer of widgets has fixed costs of $9000 per month and that the variable cost is $14 per widget (so it costs $14 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.)C = (b) Express using functional notation the total cost if there are 225 widgets produced in a month.C( )Calculate the total cost if there are 225…
The cost C (in dollars) of producing x units and the revenue R (in dollars) obtained by selling x units are shown in the figure. y 300 000 R 250 000 200 000 150000 100 000 50 000 X 1000 2000 3000 4000 5000
Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7900 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = Interpret C(200). O When this many helmets are produced the cost is $200. O This is the cost (in dollars) of producing 200 helmets. O For every additional helmet produced the cost increases by this much. O For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) =