1. Your factory produces lemon-scented candles. You know that the cost of producing each unit is lower the more candles you produce, but you also know that costs will eventually go up if you make too many candles, due to the costs of storage of the overstock. The guy in accounting says that your cost for producing x thousands of units a day can be approximated by the formula C(x)=0.04x² -8.504x+25302. However, you also know that depending on the amount that you produce, the amount that people buy also varies. The accountant tells you that your revenue can be approximated by the equation R(x) = -0.25x² +1.205x+45872. Find the production level that will maximize your profits. Text a) Determine the quadratic equation for the profit P(x) = R(x) = C(x) Text
1. Your factory produces lemon-scented candles. You know that the cost of producing each unit is lower the more candles you produce, but you also know that costs will eventually go up if you make too many candles, due to the costs of storage of the overstock. The guy in accounting says that your cost for producing x thousands of units a day can be approximated by the formula C(x)=0.04x² -8.504x+25302. However, you also know that depending on the amount that you produce, the amount that people buy also varies. The accountant tells you that your revenue can be approximated by the equation R(x) = -0.25x² +1.205x+45872. Find the production level that will maximize your profits. Text a) Determine the quadratic equation for the profit P(x) = R(x) = C(x) Text
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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Transcribed Image Text:1. Your factory produces lemon-scented candles. You know that the cost of producing each unit is lower the
more candles you produce, but you also know that costs will eventually go up if you make too many candles,
due to the costs of storage of the overstock. The guy in accounting says that your cost for producing x
thousands of units a day can be approximated by the formula C(x)=0.04x² -8.504x+25302. However,
you also know that depending on the amount that you produce, the amount that people buy also varies. The
accountant tells you that your revenue can be approximated by the equation
R(x) = -0.25x² +1.205x+45872.
Find the production level that will maximize your profits. Text
a) Determine the quadratic equation for the profit P(x) = R(x) − C(x) Text
Transcribed Image Text:b) Determine the production level needed (rounded to the nearest whole number) to earn the maximum profit
value. Text
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