Question

Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade? The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function

Answer 1

Given : Betty sets up a lemonade stand and charges $1 per glass.

It cost her $50 to set up the stand.

To Find : Which function gives the profit, p, she makes by selling g glasses of lemonade?

Solution:

The number of glasses of lemonade sold = g,  

a profit, p by function p(g)

setup cost = $50

charges for 1 glass  = 1 $

charges for g  glasses = 1.g  = g $

cost = $50  

Profit  =  g - 50  $

p(g)  =  g - 50  

p(g)  =  g - 50    is the profit function

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Answer 2

Given :-

• Total cost to Betty for Lemonade Stand = $50.
• Betty charges for a glass of Lemonade= $1 .
• P denotes = Profit.
• g denotes = No. of glasses of Lemonade Sold.

To Find :-

• Which function gives the profit, p, she makes by selling g glasses of lemonade ?

Solution :-

Since the setup cost is given $50 . we know that,

• Profit = SP - CP . { SP must be greater than CP.)

So, If Betty wants to make a profit, then,

• g > 50 .

therefore,

→ P = (No. of glasses of Lemonade Sold(g) > 50) * Charges for a glass - CP

→ P = (g > 50) * $1 - $50 .

→ P = (g - 50)

here,

• g > 50 .

hence, Set up Cost of $50 is represented by the function f(g) :-

• P = g - f(g).

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