SOLUTION: Maximum and minimum word problem Assignment 1. The school fundraising committee usually sells 1200 shirts a year at $20 each. A survey indicates that, for every $2 increase in pri

Question 175740: Maximum and minimum word problem Assignment
1. The school fundraising committee usually sells 1200 shirts a year at $20 each. A survey indicates that, for every $2 increase in price, there will be a drop of 60 sales a year.
a) Determine algebraic expressions for the price of a shirt and the number of shirts sold.
Price of shirt:
Number of shirts sold:
b)Write an equation for teh revenue, using your expressions from part (a).
Equation:
c) Use your equation from part part (b) to find out what price they should charge for each shirt to maximize the revenue.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. The school fundraising committee usually sells 1200 shirts a year at $20 each.
A survey indicates that, for every $2 increase in price, there will be a drop of 60 sales a year.
:
a) Determine algebraic expressions for the price of a shirt and the number of shirts sold.
:
Let x = no. of $2 price increases
Price of shirt: (20+2x)
Number of shirts sold: (1200-60x)
:
;
b)Write an equation for the revenue, using your expressions from part (a).
Equation: Rev = (20+2x)*(1200-60x)
FOIL
R(x) = 24000 - 1200x + 2400x - 120x^2
R(x) = -120x^2 + 1200x + 24000
:
:
c) Use your equation from part part (b) to find out what price they should
charge for each shirt to maximize the revenue.
:
Find the axis of symmetry of the above equation. a=-120; b=1200
x =
x =
x = +5
:
Price for max revenue: $20+(5*$2) = $30 per shirt for max revenue

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