Answered: P(x) = –x2 + 90x – 300 is a profit…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A cardboard box manufacturer has decided to introduce a new and improved cardboard box. The set up cost for the production of this new line is $16,600 and the variable costs are $64 per ten thousand cardboard boxes. The company expects to sell ten thousand cardboard boxes for $151. Find a function P( x) for the total profit from the production and sale of x (in ten thousands) cardboard boxes. P(x) = 151x + 16600 P(x) =151x - 16600 P(x) = 87x + 16600 P(x) = 87x - 16600
A ceramics store manufactures and sells coffee mugs. The revenue r(x) from the sale of x coffee mugs is given by r(x)=6.5x. Suppose the function for the cost of manufacturing x coffee mugs is c(x)=0.75x+1850. a. Write the profit function. b. Find the profit on 500,1000, and 5000 coffee mugs.
Suppose a gift basket maker incurs costs for a basket according to C(x)=18x+220. If the baskets are sold for $43 per basket, what is the revenue function? (Simplify the function, unsimplified will result in 0 credit) R(x)=

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P(x) = –x2 + 90x – 300 is a profit function where x is the number of items sold, and P(x) is the profit from that sale. Find the maximum profit and the number of items that must be sold to reach that profit.