The cost C (in dollars) of producing x units of a product isC= 1.70x + 9,000.(a) Find the average cost function C.C =(b) Find C when x = 1,000 and when x = 10,000.C(1,000) = $C(10,000)= $per unitper unit(c) Determine the limit of the average cost function as x approaches infinity.lim C(x) =X-00=Interpret the limit in the context of the problem.As more and more units are produced, the average cost per unit (in dollars) will approach $

Step 1: Average Cost FunctionThe average cost function, Ā(x), is the total cost divided by the…

Answered: The cost C (in dollars) of producing x…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.2: Domain And Range

Problem 61SE: The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is...

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Similar questions

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
The demand function for a commodity is p(x)=8x+50 where x is the number of unites demanded and p is the unit price. Find the revenue function and evaluate its rate of change when the level of the production is between 40 and 50.
The value of a car decreases each year. The rate at which the value decreases is called depreciation and is a represented by a percentage. For Alina buys a car for $25,000, and the depreciation rate is 25%. That means that her car’s value goes down by 25% each year. The value can be represented by the function V(y)=25000(0.75)^v, where V represents the value of her car and y represents the number of years that she owns a car. Find the depreciated value of her car if she keeps it for 5 years. In other words, evaluate: V(5)=25000(0.75)^5, rounding to the proper decimal place for money.
The price p (in dollars) and the demand x for a particular clock radio are related by the equation x=2000−20p. (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R? (C) Find the marginal revenue at a production level of 1200 clock radios. (D) Interpret R′(1600)=−60.00.
Consider a function f(x) that represents the cost, in dollars, of producing x units of a product. The revenue, in dollars, generated by selling x units of the product is given by g(x) = 100x - 2x^2. Find the production level that maximizes the profit and calculate the maximum profit.
Consider a price-demand model for tickets to see a specific hockey team play. The price p of a single-game ticket can be related to the quantity demanded, q, by the function p=148-0.01q dollars When the arena is not at full capacity the total cost for a single game (in dollars) can be expressed by the function C(q) = 54g + 50000 (a) Find marginal revenue as a function of the quantity of tickets demanded R(q) = (b) To maximize profit, the hockey team should set their ticket price to be S and we expect they will sell (c) The hockey players union has negotiated a deal requiring the team owner to pay an extra $10,000 at each game to cover safety measures and insurance What should be the new ticket price in order to ensure that profit is maximized? With the additional costs, a ticket price of $ will maximize profit game tickets at this price
The Price-Demand relation for a certain product is x = 6000 – 30 -p (a) Solve the given relation for price, p. (b) Construct the Revenue function, R(X). (C) Find the Marginal Revenue function and use it to determine the approximate change in revenues from the 90oth item sold.
The total cost of producing x units of a product is given by: and all x units will sell when the price p of each unit is: p(x) 12. C(x) 10x 100vx+ 10,000, 1000 Find functions for the marginal cost and marginal revenue of producing and selling x units of this product. Use marginal analysis to estimate the cost of producing the 101st unit. (a) (b)
0.9 The profit in dollars from the sale of x expensive watches is P(x)- 0.04x-2x+7x -5000. Find the marginal profit when (a) x=D100, (b) x- 2000, (c) x-5000 and (d) x- 10,000. (a) When x= 100, the marginal profit is $ (Round to the nearest integer as needed)
The price p (in dollars) and the demand x for a particular clock radio are related by the equation x = 5000 – 50p. (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R? (C) Find the marginal revenue at a production level of 2800 clock radios. (D) Interpret R'(3900) = – 56.00.
Marginal Average Cost for Producing Thermometers The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is represented by the following function. Find the following functions (in dollars) and interpret your results. C(x) = 2,000 + 2x (a) Find the average cost function C. C(x) = (b) Find the marginal average cost function C'. C'(x) = (c) Interpret your results. O Since the marginal average cost function is negative for x > 0, the rate of change of the average cost function is negative for all x > 0. O Since the marginal average cost function is negative for x > 0, the rate of change of the average cost function is positive for all x > 0. O Since the marginal average cost function is positive for x > 0, the rate of change of the average cost function is positive for all x > 0. O Since the marginal average cost function is positive for x > 0, the rate of…
The cost in dollars of producing alarm clocks is given by C(x) = 50x³ – 750x²+ 3740x +3750, where x is in units of 1000. (a) Calculate the average cost at x = 4, 6, 8, and 10. (b) Use the graphical interpretation of average cost to find the produc- tion level xo at which average cost is lowest. What is the relation between average cost and marginal cost at xo (see Figure 16)? C (S) 15,000 - 10,000 - 5000 1 2 3 4 5 6 7 8 9 10 FIGURE 16 Cost function C(x) = 50x³ – 750x² + 3740x + 3750.

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