Concept explainers
Internet Purchases An Internet bookstore charges $15 shipping for orders under $100 but provides free shipping for orders of $100 or more. The cost C of an order is a function of the total price x of the books purchased, given by
- (a) Find C(75), C(90), C( 100), and C(105).
- (b) What do your answers in part (a) represent ?
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- Volume of a Box An open box is to constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shownin figure. (a) Express the volume V of the box as a function of x. (b) What is the domain of V? (Use the fact that length and volume must be positive.) (c) Draw a graph of the function V, and use it to estimate the maximum volume for such a box.arrow_forwardBusiness The annual cost C (in thousands of dollars) and revenue R (in thousands of dollars) for a company each year from 2010 through 2016 can be approximated by the models C=2549t+1.1t2andR=341+3.2t where P is the year, with t=10 corresponding to 2010. (a) Write a function P that represents the annual profit of the company. (b) Use a graphing utility to graph C,R, and P in the same viewing window.arrow_forwardProfit The profit P, in thousands of dollars that a manufacturer makes is a function of the number N of items produced in a year, and the formula is P=0.2N2+3.6N9. a. Express using functional notation the profit at a production level of 5 items per year, and then calculate that value. b. Determine the two break-even points for this manufacturesthat is, the two production levels at which the profit is zero. c. Determine the maximum profit if the manufacturer can produce at most 20 items in a year.arrow_forward
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