Since the pandemic hit the United States, a retailer has been selling 1200 tablets each week at $425 each. The marketing department estimates that an additional 75 tablets per week will sell for every $15 the price per tablet is lowered. Use Calculus to determine the price per tablet that will maximize revenue. What is the maximum revenue?

Since the pandemic hit the UnitedStates,a retailerhas been selling 1200 tablets each week at $425 each.The marketing department estimates that an additional75 tablets per week will sell for every $15 the price pertablet is lowered. Use Calculus to determine the price pertablet that will maximize revenue.What is the maximum revenue?The retailer sells 1200 tablets each week at $425and the marketing department estimates that an additional75 tablets per week will sell for every $15 the price pertablet is lowered.Hence,the retailer sells 1275 tabletseach week at$410.therefore,1200tablets$425each1275tablets$410eachNow,wecanestablishrelationshipbetweentabletsanditsprice.Then,T-1200=1275-1200410-425P-425T-1200=75-15P-425⇒T=-5P+3325Further,RP=PTPRP=P-5P+3325=-5P2+3325PTake first derivative,thenR'P=-10P+3325Put R'P=0,then-10P+3325=0P=$332.5Now,R''P=-5<0.Hence, the revenue will be maximize at the price P=$332.5.Therefore, the maximum revenue will be Maximum revenueR(P)=-5(332.5)2+3325(332.5)=$552,781.25

Answered: Since the pandemic hit the United States, a retailer has been selling 1200 tablets each week at $425 each. The marketing department estimates that an additional…

Advanced Engineering Mathematics

10th Edition

ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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Since the pandemic hit the United States, a retailer has been selling 1200 tablets
each week at $425 each. The marketing department estimates that an
additional 75 tablets per week will sell for every $15 the price per tablet is
lowered. Use Calculus to determine the price per tablet that will maximize
revenue. What is the maximum revenue?
*Be sure to use a sign chart to demonstrate you have a maximum.

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