Concept explainers
Advertising and sales After hiring a new VP for advertising, a company predicts that sales will increase and that the yearly sales will be given by the equation
(a) What are the sales when the new VP begins?
(b) What are the predicted sales for the third year?
(c) What are the maximum predicted sales?
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Chapter 5 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
- 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?arrow_forwardHeight of a Ball If a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y=40t16t2 . What is the maximum height attained bythe ball?arrow_forwardFalling Ball Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 128 ft high, then its height h above the ground t seconds later will be h=128+16t-16t2 During what time interval will the ball be at least 32 ft above the ground?arrow_forward
- Decomposing Functions To join a book club, you pay an initial fee and then a fixed price each month for a book. The total cost in dollars of joining the club and buying n books is given by C=30+17n. What is the initial fee? What is the cost of each book after you are a club member?arrow_forwardMaximum Profit The profit P (in dollars) generated by selling x units of a certain commodity ¡s given by P(x)=1500+12x0.0004x2 What is the maximum profit, and how many units must be sold to generate it?arrow_forwardFlood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forward
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