SOLUTION: the financial manager of a college newsletter determine that 1000 copies of the newsletter will be sold if the price is 50 cents and that the number of copies sold decrease by 10 f
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Question 900237: the financial manager of a college newsletter determine that 1000 copies of the newsletter will be sold if the price is 50 cents and that the number of copies sold decrease by 10 for each 1 cent added to the price. What price will yield the largest gross income from sales and what is the largest gross income?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
the financial manager of a college newsletter determine that 1000 copies of the newsletter will be sold if the price is 50 cents and that the number of copies sold decrease by 10 for each 1 cent added to the price. What price will yield the largest gross income from sales and what is the largest gross income?
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let x=number of 1 cent price increases
Revenue=price*copies sold
R(x)=(50+x)(1000-10x)=50000+500x-10x^2
-10x^2+500x+50000
-x^2+50x+5000
complete the square:
-(x^2-50+625)+625+5000
R(x)=-(x-25)^2+5625
This is an equation of a parabola that opens down with vertex at (25,5625)
What price will yield the largest gross income from sales: $25
What is the largest gross income? $5625
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