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Question 802033: Hello tutor,
Can you please help me solve this following problem.
The revenue function for a gourmet cupcake is given by R(x)=-40x^2+15x+350, where x is the price of one cupcake in a dollars. The cost function is C(x)=150-5x. Determine the price of one cupcake that will allow the bakery to break even.
Thanks.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The revenue function for a gourmet cupcake is given by R(x)=-40x^2+15x+350, where x is the price of one cupcake in a dollars.
The cost function is C(x)=150-5x.
Determine the price of one cupcake that will allow the bakery to break even.
:
Breakeven occurs when cost = revenue, therefore
150 - 5x = -40x^2 + 15x + 350
Combine like terms on the left
40x^2 - 5x - 15x + 150 - 350 = 0
40x^2 - 20x - 200 = 0
Simplify, divide by 20
2x^2 - x - 10 = 0
Factors to
(2x-5)(x+2) = 0
the positive solution is all we want here
2x = 5
x = $2.50!
:
See if that works
150-5(2.5) = $137.50 in cost
and
-40(2.5^2) + 15(2.5) + 350 = 137.5
-250 + 37.5 + 350 = $137.50 in revenue
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