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: 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
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