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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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Chapter 3 Solutions
College Algebra: Graphs and Models (6th Edition)
- 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_forwardThe cost C and the revenue R for a brokerage firm depend on the number T of transactions executed. (Both C and R are measured in dollars.) It costs $710 per day to keep the office open, and brokers are paid an average of $24 per transaction. Also, $34 in fees are collected for each transaction.arrow_forward
- Need asap pls. Thanks.arrow_forwardThe figure to the right shows the U.S. demand and supply for leather footwear. Under autarky, the producer surplus is area OA. V OB. S+T+V+W+X OC. T+W+X. OD. S + V Price $54 30 24 0 R S V W X TU Q Q₁ Y Q₂ US Supply World price US Demand Quantity of leather footweararrow_forwardThe equation below best describes which role of health? T =6-TS=TW+T?+ TH a. Health as a consumption good, because health enables work, which yields income. O Health as an input into production, because sick time detracts from productive time. Oc. Health as an input into production, because productive time enters directly into the utility function. O Health as an investment, because time spent working yields future income.arrow_forward
- Newborn blue whales are approximately 24 feet long and weigh 3 tons. Young whales are nursed for 7 months, and by the time of weaning they often are 58 feet long and weigh 19 tons. Let L and W denote the length (in feet) and the weight (in tons), respectively, of a whale that is t months of age. (a) If L and t are linearly related, express L in terms of t. (b) What is the daily increase in the length of a young whale? (Use 1 month = 30 days. Round your answer to three decimal places.) ________ ft/day (c)If W and t are linearly related, express W in terms of t. (d) What is the daily increase in the weight of a young whale? (Round your answer to three decimal places.) __________tons/dayarrow_forwardThe revenue function of a company that sells its product at a fixed price 220 OMR per unit and the variable cost of producing one unit is 200 OMR Select one: O A. R(x) = 200x + 220 O B. R(x) = 220x – 200 OC R(x) = 220x O D. R(x) = 220x + 200 %3Darrow_forwardE1arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
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