SOLUTION: 2. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. a. Write

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 2. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. a. Write       Log On


   

Question 228146: 2. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups.
a. Write an equation for the number of cups you sell as a function of the price you charge.
b. Denote "C" for number of cups, and "P" for the price you charge.
c. Assume the function is linear.

3. Continuing our lemonade stand question:
a. We all know that total revenue (TR) is a function of the price we charged (P) multiplied by the item quantity sold (in our case – Cups), i.e., TR = Price * Cups
b. Please write the equation for your TR by inputting your answer from the function you have calculated in question #2.
c. What price would maximize your TR?


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups.
a. Write an equation for the number of cups you sell as a function of the price you charge.
You have two points relating cups sold and price: (120,2)(60,3)
slope = (2-3)/(120-60) = -1/60
Since 2 = (-1/60)*120+b, b = 2+2 = 4
Equation:
P = (-1/60)c + 4
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b. Denote "C" for number of cups, and "P" for the price you charge.
c. Assume the function is linear.
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3. Continuing our lemonade stand question:
a. We all know that total revenue (TR) is a function of the price we charged (P) multiplied by the item quantity sold (in our case – Cups), i.e., TR = Price * Cups
b. Please write the equation for your TR by inputting your answer from the function you have calculated in question #2.
TR = c
TR = (-1/60)c^2 + 4c
Note: This is a quadratic with a = (-1/60) and b = 4
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c. What price would maximize your TR?
Max occurs when c = -b/2a = -4/(-2/60) = 120 cups
P(120) = $2 so a price of $2 gives you maximum revenue.
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Cheers,
Stan H.