SOLUTION: Can anyone help me with this? Suppose you own a strip mall. You want to determine the amount of rent you should charge to maximize your profit. The given equation measure the pro

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Question 473563: Can anyone help me with this?
Suppose you own a strip mall. You want to determine the amount of rent you should charge to maximize your profit. The given equation measure the profit, P (is in thousands of dollars), per square foot of rental space (m is dollars per square foot).
P(d) = -8.3m^2 + 53.1m - 26.5
1. Does the graph of this equation open up or down? What algebraic information can you use to determine this?
2. Describe what happens to the profit as the rent per square foot is increased. Discuss the different amounts of profit defined by the graph and the equation.
3. Use the quadratic formula to determine the amounts that should be charged for rent that will give you zero profit. Round the value of m to the nearest tenth of a square foot.
What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
4. Will this equation give you a maximum profit or a minimum profit? How do you know?
5. What price should be charged to reach the maximum or minimum profit?
6. How much profit will you have at the peak or low? Remember that the profit is measured in thousands of dollars. Include the proper units.
7. What is the point of the vertex? Calculate this value. How does this number relate to your answers in numbers 5 and 6?
8. How many solutions are there to the equation ? How do you know? Give an algebraic and a written response.

Answer by stanbon(57356) (Show Source):
You can put this solution on YOUR website!
Suppose you own a strip mall. You want to determine the amount of rent you should charge to maximize your profit. The given equation measure the profit, P (is in thousands of dollars), per square foot of rental space (m is dollars per square foot).
P(d) = -8.3m^2 + 53.1m - 26.5

1. Does the graph of this equation open up or down? What algebraic information can you use to determine this?
Ans: Opens down because the coefficient of x^2 is negative.
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2. Describe what happens to the profit as the rent per square foot is increased. Profit rises then falls as square footage increases.
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Discuss the different amounts of profit defined by the graph and the equation.
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3. Use the quadratic formula to determine the amounts that should be charged for rent that will give you zero profit. Round the value of m to the nearest tenth of a square foot.
Solve -8.3m^2 + 53.1m - 26.5 = 0
m = 0.5456 ; m = 5.852
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What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
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4. Will this equation give you a maximum profit or a minimum profit? How do you know?
Maximum because it has a peak.
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5. What price should be charged to reach the maximum or minimum profit?
m = -b/(2a) = -53.1/(2*-8.3) = 3.20
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6. How much profit will you have at the peak or low? Remember that the profit is measured in thousands of dollars. Include the proper units.
$58,428
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7. What is the point of the vertex? Calculate this value. How does this number relate to your answers in numbers 5 and 6?
They are the same
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8. How many solutions are there to the equation ? How do you know? Give an algebraic and a written response.
Two because the equation is a quadratic.
The discriminant is positive so there are 2 Real Number solutions.
Cheers,
Stan H.