SOLUTION: Peter has 40 pumpkins to sell. He will sell them all if he sets his price at $1.00 each, but will sell one less pumpkin for each 5 cent increase in price. What price should he char
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Question 66187: Peter has 40 pumpkins to sell. He will sell them all if he sets his price at $1.00 each, but will sell one less pumpkin for each 5 cent increase in price. What price should he charge to maximize his earnings?(Show algebraically)
You can put this solution on YOUR website! Peter has 40 pumpkins to sell. He will sell them all if he sets his price at $1.00 each, but will sell one less pumpkin for each 5 cent increase in price. What price should he charge to maximize his earnings?
:5
Then amt sold will be (40-x); the price will be (1+.05x), y = total earnings
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y = pumpkins sold * price:
y = (40-x)(1+.05x)
FOIL
y = 40 + 2x - 1x - .05x^2
y = 40 + x - .05x^2
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Put it in the standard y = ax^2 + bx + c form:
y = -.05x^2 + x + 40
:
The max revenue(y) will occur at the vertex. Vertex equation: x = -b/(2a)
In our equation a=-.05; b= 1
x = -1/(2*-.05)
x = -1/-.1
x = 10
That means that the cost = $1 + (10*.05) = $1.50 a piece for max earnings
Number of pumpkins sold will be 40 - 10 = 30 pumpkins sold at that price
Total revenue: 30 * 1.50 = $45
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A graphical presentation will make it clear to you:
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Notice that the max earnings occurs when x = 10
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He only needs to sell 30, that leaves 10 that he can give away or make pies or something, right?
