This is my word problem. Thank you.  The accounting department at Factory Shoe has determined that the quadratic relation P=-2x2+24x-54 models the company’s profit. In this equation, P represents the profit (in $100 000s) and x represents the number of pairs of shoes sold (in 100 000s). a. Write the equation in factored form.  b. What are the zeros of the relation? What do they represent?  c. Calculate the number of pairs of shoes that the company must sell to maximize its profit. How much would that maximum be?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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This is my word problem. Thank you. 

The accounting department at Factory Shoe has determined that the quadratic relation P=-2x2+24x-54 models the company’s profit. In this equation, P represents the profit (in $100 000s) and x represents the number of pairs of shoes sold (in 100 000s).

a. Write the equation in factored form. 

b. What are the zeros of the relation? What do they represent? 

c. Calculate the number of pairs of shoes that the company must sell to maximize its profit. How much would that maximum be? 

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