5) A company manufactures and sells x e-book readers per month. Themonthly cost and price-demand equations areC(x) = 350x +40,000p= 500-0.025xa) Find the profit functionb) Find the maximum monthly profit. How many readers should thecompany manufacture and how much should charge for each reader tomaximize its profit?

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Description: 5) A company manufactures and sells x e-book readers per month. Themonthly cost and price-demand equations areC(x) = 350x +40,000p= 500-0.025xa) Find the profit functionb) Find the maximum monthly profit. How many readers should thecompany manufactu

Given Monthly cost equation Cx=350x+40000Price demand equation p=500-0.025xPart (a) Profit function=px-CxProfit function=500-0.025xx-350x+40000Profit function=500x-0.025x2-350x-40000Profit function=-0.025x2+150x-40000 ......1part bfrom equation 1,-0.025x2+150x-40000=0differentiate with respect to x, we have-0.05x+150=0x=1500.05x=3000Thus from equation 1Maximum monthly profit=-0.02530002+150×3000-40000Maximum monthly profit=185000and 3000 reader should the company manufacture.and Charge for each reader=500-0.025×3000Charge for each reader=425So $425 Charge for each reader.

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5) A company manufactures and sells x e-book readers per month. The monthly cost and price-demand equations are C(x) = 350x+40,000 a) Find the profit function b) Find the maximum monthly profit. How many readers should the p= 500-0.025x company manufacture and how much should charge for each reader to maximize its profit?

5) A company manufactures and sells x e-book readers per month. The monthly cost and price-demand equations are C(x) = 350x+40,000 a) Find the profit function b) Find the maximum monthly profit. How many readers should the p= 500-0.025x company manufacture and how much should charge for each reader to maximize its 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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5) A company manufactures and sells x e-book readers per month. The
monthly cost and price-demand equations are
C(x) = 350x +40,000
p= 500-0.025x
a) Find the profit function
b) Find the maximum monthly profit. How many readers should the
company manufacture and how much should charge for each reader to
maximize its profit?

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