Maximizing Profit. In business, profit is the difference between revenue and cost; that is,
where x is the number of units sold. Find the maximum profit and the number of units that must be sold in order to yield the maximum profit for each of the following.
R(x) = 50x − 0.5x2, C(x) = 10x + 3
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COLLEGE ALGEBRA (PRINT UPGRADE)
- Demand A company has found that the daily demand x for its boxes of chocolates is inversely proportional to the price p. When the price is $5, the demand is 800 boxes. Approximate the demand when the price is increased to $6.arrow_forwardMarket supply The following table shows the quantity S of wheat, in billions of bushels, that wheat supplies are willing to produce in a year and offer for sale at a price P, in dollars per bushel. S = quantity of wheat P = price 1.0 1.35 1.5 2.40 2.0 3.45 2.5 4.50 In economics, it is customary to plot S on the horizontal axis and P on the vertical axis, so we will think of S as a variable and of P as a function of S. a. Show that these data can be modeled by a linear function, and find its formula. b. Make a graph of the linear formula you found in part a. This is called the market supply curve. c. Explain why the market supply curve should be increasing. Hint: Think about what should happen when the price increases. d. How much wheat would suppliers be willing to produce in a year and offer for sale at a price of 3.90 per bushel?arrow_forwardFind the constant of proportionality. R is inversely proportional to the square of I. If I=25, then R=100.arrow_forward
- Doctors treated a patient at an emergency room from 2:00P.M. to 7:00P.M. The patient’s blood oxygen level L (in percent) during this time period can be modeled by L=0.270t2+3.59t+83.1,2t7 where t represents the time of day, with t=2 corresponding to 2:00P.M. Use the model to estimate the time (rounded to the nearest hour) when the patient’s blood oxygen level was 93 .arrow_forwardFind the constant of proportionality. E varies jointly with I and R. If R=25 and I=5, then E=125.arrow_forwardX(in mph) 20 30 40 50 60 65 70 Y(in feet) 815 1090 1485 1840 2140 2315 2490 complete questionsarrow_forward
- Use the information given in the figure below to construct a mathematical model for the number of pounds of salt x₁(t), x₂(t), and x3(t) at time t in tanks A, B, and C, respectively. dx₁ dt dx2 dt dx3 dt = = = pure water 5 gal/min A 100 gal mixture 4 gal/min mixture 9 gal/min B 100 gal mixture 1 gal/min mixture 6 gal/min C 100 gal mixture 5 gal/minarrow_forwardrelationship between temperature measured in the Celsius scale and the Fahrenheit scale is linear. The freezing point is gC and 32F, and the boiling point is 212°F, respectively. Find F as a function of C and use this formula to determine the temperature in Fahrenheit corresponding to temperature of15 C a. 60 F O b. 59 F DC 61 F Dd. 62 F QUESTION 3 The quantity demanded for a certain brand of portable CD players is 200 units when the unit price is set at $90. The quantity demanded is 1,200 units when the unit pric is $40. Find the demand equation. O a.p=.0.05x-90 Ob.p=-0.05x- 100 Oc.p=-0.04x-90 O d.p=.0.04x-100 QUESTION 4 Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx - b. 6x -9y + 8-0 O a. y- 6x -8 Click Save and Submit to save and submit. Click Save AIL Ansuers to saue all answers.arrow_forwardThe time t that it takes to get to schoolvaries inversely with your average speed s.(a) Suppose that it takes you 40 minutes to get to schoolwhen your average speed is 30 miles per hour. Expressthe driving time to school in terms of average speed.(b) Suppose that your average speed to school is 40 milesper hour. How long will it take you to get to school?arrow_forward
- The cost C, in dollars, of a prepaid cell phone call is proportional to the time t, in minutes, that the call lasts. The equation that represents this relationship for carrier A is C-0.15t. The table shows the relationship for carrier B. Which carrier has a lower unit rate? Time Cost (minutes) (dollars) 0.24 0.60 1.20 5n 10 30 3.60 Carrier A Carrier B Carrier A and Carrier B have the same unit rate The relationship can't be determinedarrow_forwardE1arrow_forwardBoyle’s Law says that the volume V of a gas atconstant temperature increases whenever the pressure P decreases,so that V and P are inversely proportional. If P = 14.7 lb>in2 whenV = 1000 in3, then what is V when P = 23.4 lb/in2?arrow_forward
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