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Question 1191133: A school club makes and sells decorations to raise money. The materials for each decoration cost
$6, and the club sells them for $10 each. They sell 20 decorations per week. They are considering
raising the price, so they conduct a survey and find that for every dollar increase, they will lose 2
sales per week. Set up a function and solve to determine what price they should charge to maximize
profits.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Their profit is $4 per sale currently
for each $1 increase they lose 2 sales.
profit is 4+x, and sales are 20-2x
so maximize that profit which is f(x)= 80+12x-2x^2
x=-b/2a maximum or -12/-4 or 3, and f(3)=80+36-18=$98
so when x=3 the sale price is $13 (profit is $7) and the sales number is 14 (20-3*2)
The profit is maximum $98 at $13 per decoration sale price.
Check
#---price-#---revenue-- N-CP(number-cost to produce)---Profit
6---$10---20--$200------$120-----------------------------$80
6---$11---18---$198----- $108-----------------------------$92
6---$12---16--$192------$96------------------------------$96
6---$13---14--$182------$84------------------------------$98
6---$14---12--$168------$72------------------------------$96
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