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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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
Transcribed Image Text:Break-Even Analysis You are setting up a part-time business with an initial investment of $24,000. The unit cost of the product is $11.80, and the selling price is $19.30.
(a) Find equations for the total cost C (in dollars) and total revenue R (in dollars) for x units.
C(x) =
R(x) =
(b) Find the break-even point by finding the point of intersection of the cost and revenue equations.
units
(c) How many units would yield a profit of $1,000?
units
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- Producing x footballs costs C(x) = 2.5x +500. If each football sells for $22.50, determine the break-even quantityarrow_forwardMaximizing Profits A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x rackets/day is given by C(x) = 600 + 2x + 0.0003x2. Each racket can be sold at a price of p dollars, where p is related to x by the demand equation p = 9 -0.0002x. If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer. Hint: The revenue is R(x) = px, and the profit is P(x) = R(x) C(x). racketsarrow_forwardA manufacturer has a total cost function C(x) = 3.5x + 1000 and a revenue function R(x) = 4.75x. (a) The revenue at the break-even point is No comma. No space. No $ sign. (b) What quantity must be sold for the manufacturer to make a profit of $6500? No comma. No space. unitsarrow_forward
- At Lincoln Library there are two ways to pay for copying. You can pay 6 cents a copy, or you can buy a plastic card for $7 and then pay 5 cents a copy. Let x be the number of copies you make. Write an equation for your costs for each way of paying. (Express C(x) in dollars.) without card C(x) = with card C(x) = (a) How many copies do you need to make before buying the plastic card is the same as cash? copies(b) If you wish to make 699 copies, which way of paying has the least cost? they are the samecannot be determined without cardwith cardarrow_forwardAn electronics company is planning to manufacture a new line of high-end noise reduction ear buds. Fixed costs will be $123,000 and it will cost $13 to produce each pair of ear buds. The ear buds will sell for $43 a pair. Using the equations for cost C and revenue R as given below where x represents the units of product, find the break-even point for producing the new ear buds. C(x)=fixed cost+(cost per unit produced)•x R(x)=(price per unit sold)•x What is the break-even point?arrow_forward
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