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Question 277463: Please help me solve this problem: 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. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for the number of cups, and "P" for the price you charge. Assume the function is linear.
Continuing our lemonade stand question:
We all know that local revenue (TR) is a function of the price we charge (P) multiplied by the item quantity sold (in our case-Cups),i.,e.,TR=Price*Cups.
Please write the equation for your TR by inputting your answer from the function you have calculated. What price would you maximize your TR?
Answer by stanbon(75887)   (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. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for the number of cups, and "P" for the price you charge. Assume the function is linear.
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You have two points relating price and cups sold: (2,120) and (3,60)
Equation you want: C = mp + b where p is price and C is # of cups.
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slope = m = (120-60)/(2-3) = -60
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60 = -60*3 + b
b = 4*60
b = 240
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Equation: # of cups sold = -60p + 240
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Continuing our lemonade stand question:
We all know that local revenue (TR) is a function of the price we charge (P) multiplied by the item quantity sold (in our case-Cups),i.,e.,TR=Price*Cups.
Please write the equation for your TR by inputting your answer from the function you have calculated. What price would you maximize your TR?
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Total Revenue = -60p^2 + 240p
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This is a quadratic equation with a = -60 and b = 240
Maximum occurs when p = -b/2a = -240/(-120) = 2
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Maximum sales occurs when the price is $2.
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Cheers,
Stan H.
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