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
Answers
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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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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