Advanced Functions Question?

[匿名]

2018-01-23 11:04 am

Amy has a business selling lemonade. She pays $35 per day to rent her space and each cup of lemonade costs her $1. She sells each cup at $2.50 and brings enough lemonade to sell a maximum of 200 cups per day.

a) Write an equation to model her total cost, C, for 1 day as a function of number of cups, n, of lemonade sold.

my answer: C (n) = n + 35

b)Write an equation to model her total revenue, R, for 1 day as function of number of cups, n, of lemonade sold.

my answer: R (n) = 2.50n

c) Develop an algebraic expression for the profit function, P(n). What is Amy's break even point? What is her maximum possible profit she can earn in one day?
I need help with c)

回答 (1)

不用客氣

2018-01-23 11:24 am

✔ 最佳答案

The answers in a) and b) are correct.

c)
P(n) = R(n) - C(n)
P(n) = 2.50n - (n + 35)
P(n) = 1.5n - 35

At the break even point : P(n) = 0
1.5n - 35 = 0
n = 23.33
However, n must be integer. Therefore, she gets loss when n ≤ 23, but gets profit when n ≥ 24.

P(n) = 1.5n - 35
The greater the value of n, the greater the value of P(n).
Hence, P(n) is maximum when n reaches its maximum, i,.e. maximum n = 200
Maximum P(n) = 1.5(200) - 35 = 265
Maximum profit she can earn in one day = $265

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