Profit Functions A company has a fixed cost of $26,000 and a production cost of $5 for each unit it manufactures. A unit sells for $10. Find the following functions (in dollars). (a) What is the cost function? C(x) = (b) What is the revenue function? R(x) = (c) What is the profit function? P(x) = (d) Compute the profit (loss), in dollars, corresponding to the following production levels. P(5,500) = $ P(8,800) = $ P(12,100)

Profit Functions A company has a fixed cost of $26,000 and a production cost of $5 for each unit it manufactures. A unit sells for $10. Find the following functions (in dollars). (a) What is the cost function? C(x) = (b) What is the revenue function? R(x) = (c) What is the profit function? P(x) = (d) Compute the profit (loss), in dollars, corresponding to the following production levels. P(5,500) = $ P(8,800) = $ P(12,100)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section4.2: Complex Solutions Of Equations

Problem 79E: Profit The demand equation for a microwave oven is given by p=1400.0001x, where p is the unit price...

See similar textbooks

Similar questions

Concentration of a Mixture A 1000-liter tank contains 50 liters of a 25brine solution. You add xliters of a 75brine solution to the tank. (a) Show that the concentration C, the proportion of brine to total solution, in the final mixture is C=3x+504(x+50). (b) Determine the domain of the function based on the physical constraints of the problem. (c) Sketch the graph of the concentration function. (d) As the tank is filled, what happens to the rate at which the concentration of brine is increasing? What percent does the concentration of brine appear to approach?
Drug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?
Size of High Schools The farm population has declined dramatically in the years since World War II, and with that decline, rural school districts have been faced with consolidating in order to be economically efficient. One researcher studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 in enrollment. He considered the cost per pupil as a function of the number of pupils enrolled in the high school, and he found the approximate formula C=7430.402n+0.00012n2 where n is the number of pupils enrolled and C is the cost, in dollars, per pupil. a. Make a graph of C versus n. b. What enrollment size gives a minimum per-pupil cost? c. If a high school had an enrollment of 1200, how much in per-pupil cost would be saved by increasing enrollment to the optimal size found in part b?
Break-even Point A manufacturer of T-shirts has fixed costs of 3500 per month. These are monthly costs that are incurred no matter how many T-shirts are produced. These are variable costs of 8 per T-shirt. That is, it costs 8 to produce each additional T-shirt. T-shirts sell for 10 each. a. The cost function gives the cost C, in dollars, of producing t T-shirts per month. Find a formula for the cost function. b. The revenue function gives the revenue R, in dollars, obtained from selling t T-shirts. Find a formula for the revenue function. c. The break-even point is the number of T-shirts produced and sold that results in a net income of 0 dollars. That is when cost equals revenue. Find the break-even point for this manufacturer.
Profit The demand equation for a microwave oven is given by p=1400.0001x, where p is the unit price (in dollars) of the microwave oven and x is the number of units sold. The cost equation for the microwave oven is C=80x+150,000, where C is the total cost (in dollars) and x is the number of units produced. The total profit P obtained by producing and selling x units is modeled by P=xpC. (a) Find the profit function P in terms of x. (b) Find the profit when 250,000 units are sold. (c) Find the unit price when 250,000 units are sold. (d) Find (if possible) the unit price that will yield a profit of 10 million dollars. If not possible, explain why.
Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?