The cost, in dollars, to produce a designer dog leashes is C(x) = 3x + 9, and the price-demand functionin dollars per leash, is p(x) = 117 - 3xFind the revenue function R(x). (Hint: Revenue is found by multiplying the price function by the numberof units produced/sold.)R(x) =Find the profit function P(x). (Hint: Profit is found by subtracting cost from revenue.)P(x) =Find the number of leashes which need to be sold to maximize the profit.Oleashes05Find the maximum profit.ᏅdollarsFind the price to charge per leash to maximize profit.dollarsOF

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Answered: The cost, in dollars, to produce a…

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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4. It costs C(x) = 112 + 1.4x dollars to produce x Specialty Hair Ribbons. To sell x Specialty Hair Ribbons, the price should be set at p(x) = 18 - 0.2x. a.Find the revenue function R(x) and the profit function P(x) when the manufacturer makes and sells x ribbons. Simplify your functions. R(x) P(x) b. How many ribbons should be made and sold to break even? Round your answers) to the nearest whole number and include units. What profit (or loss) does the manufacture incur when they make and sell 32 ribbons? Circle profit or loss and fill in the blank below rounding to the nearest whole dollar. At a production level of 32 Ribbons, they have a profit / 1OSS of
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A dinner concert is held in Salzburg to raise funds for a local music school. The event organiser pays $8,000 to rent a venue and $12,000 to hire the musicians, as well as an additional fee of $40 per concert-goer to cover the cost of food and drink. The tickets are sold at $200 each. (a) Define an appropriate variable x, and write down the cost function C(x) for the event organiser. (b) Write down the revenue function R(x) for the event organiser. (c) Find the number of concert-goers needed for the organiser to break even. (d) Find how many people must attend the concert for the organiser to realise a profit of $8,000.
A company can manufacture at most 200 units per month. About x units per month can be sold at the price p(x) = (500 – x) dollars and the cost of producing x units per week is C(x) = 150 + 4x + x2 dollars. Find; a. Revenue from sale of x units per week b. Maximum weekly profit and the number of units produced to obtain the maximum d. Marginal Revenue at Maximum weekly profit level c. Marginal cost functions at Maximum weekly profit level
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A piano manufacturer has a daily fixed cost of $1,700 and a marginal cost of $2,100 per piano. Find the cost C(x) of manufacturing x pianos in one day. C(x) = 2100 + 1700 X Use your function to answer the following questions. (a) On a given day, what is the cost of manufacturing three pianos? $8000 That's it! (b) What is the cost of manufacturing the third piano that day? $ 2100 Nicely done. (c) What is the cost of manufacturing the 11th piano that day? $ 2100 Excellent! (d) What is the variable cost? $ What is the fixed cost? $ What is the marginal cost? $ X per piano
A Midwestern factory has been studying their costs and estimates the total cost for an upcoming production run can be modeled by C(x) = 41000 + 80x + x³ dollars. The total revenue from the sale of x units is R(x) = 3680x dollars. Before they start production, they want to know if it will be worthwhile... That is, can they make money? (a) Find the profit function, (b) determine the level of production that will maximize profit, and (c) find the maximum profit possible according to this model. a) The profit function is P(x) = Round the production level to the nearest whole unit. b) The production level per week that results in the maximum profit is Use the whole number you entered above to compute the maximum profit. c) The maximum profit is $
Your college newspaper, The Collegiate Investigator, has fixed production costs of $72 per edition and marginal printing and distribution costs of 39¢ per copy. The Collegiate Investigator sells for 49¢ per copy. (a) Write down the associated cost function C(x) in dollars. C(x) = Write down the revenue function R(x) in dollars. R(x) = Write down the profit function P(x) in dollars. P(x) = (b) What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator? $ (c) How many copies should be sold in order to break even? copies

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