Homework Help

A boy is selling lemonade throughout the hot summer. Suppose the number of cups sold is...

user3666642's profile pic

Posted via web

dislike 1 like

A boy is selling lemonade throughout the hot summer. Suppose the number of cups sold is given by the function, `n(X)=x2^(-x)+2` , where the price, x, in dollars determines the number of cups sold per day, n, in hundreds.

a)  What is the price that maximizes the number of cups sold?

b)  How many cups are sold at this price?

1 Answer | Add Yours

crmhaske's profile pic

Posted (Answer #2)

dislike 1 like

In order to determine the maximum number of cups sold, we need to first find for what value of x (price) n(x) is maximized.  To do so, first take the derivative of n(x):

`n'(x)=2^(-x)-x2^(-x)ln(2)`

Now set the derivative to 0 and solve for x:

`0=2^(-x)-x2^(-x)ln(2)`

`0=1-xln(2)`

`x=1/ln(2)=1.44`

a) Therefore, if they are sold at $1.44 the number sold is maximized.

b) `n(1.44)=1.44*2^(-1.44)+2=2.53~~3`

Approximately 3 cups are sold at a price of $1.44

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes