The Acme Widget Company has found that if widgets are priced at $245, then 4800 will be sold each month. They have also found that for every increase of $20, there will be 100 fewer widgets sold each month. The cost to produce each widget is $73.5 plus the monthly fixed costs are $1800.

The Acme Widget Company has found that if widgets are priced at $245, then 4800 will be sold each month. They have also found that for every increase of $20, there will be 100 fewer widgets sold each month. The cost to produce each widget is $73.5 plus the monthly fixed costs are $1800.

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: Solution

Question

The Acme Widget Company has found that if widgets are priced at $245, then 4800 will be sold each
month. They have also found that for every increase of $20, there will be 100 fewer widgets sold each
month. The cost to produce each widget is $73.5 plus the monthly fixed costs are $1800.
Find the price that will maximize profits from the sale of widgets (round to the nearest cent)
$
At this price, what is the maximal monthly profit? (round to the nearest dollar)
How many widgets must be sold each month to earn the maximum profit? (round to the nearest whole
number)

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