SOLUTION: A club 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. What price they should charge

Question 196967: A club 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. 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!
A club 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.
What price they should charge for each shirt to maximize the revenue?
:
Let x = no. of $2 increases
also
Let x = no. 60 shirt sales reductions
:
Price = (20 + 2x)
No. of shirts = (1200 - 60x)
:
Revenue = price * no. of shirts sold, therefore:
R = (20 + 2x)*(1200 - 60x)
FOIL
R = 24000 - 1200x + 2400x - 120x^2
Arranges as a quadratic equation
R = -120x^2 + 1200x + 24000
Find the axis of symmetry to find the price for max revenue: x = -b/(2a)
In this equation; a=-120; b=1200
x =
x =
x = +5 ea $2 increases
and
5*60 = 300 reduction in shirt sales:
:
Price for max sales; 20 +2(5) = $30, will sell 1200 - 300 = 900 shirts
:
Max revenue: 30 * 900 = $27,000
;
:
How about this? Did this make sense to you?

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