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
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1. The school fundraising committee usually sells 1200 shirts a year at $20 each. A survey indicates that, for every $2 increase in pri
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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.
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
