Cost, Revenue, Profit
Identify the relevant information given to you in the application problem below. Use that information to answer the questions that follow on cost, revenue and profit.
Round your answers to two decimal places as needed.
You decide to begin selling frozen bananas at the local park. Your cost for each frozen banana is $2.25 plus you have to pay a fixed weekly fee of $120 for the booth. Your plan is to sell each frozen banana for $3.51.
1. Write a function, Cin), to represent your total costs for the week if you sell n frozen bananas. C(n) 2.25 + 120
2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week. R(n) 3,5ln
3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week. P(n) 1.26n - 120
1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number. 95.23809524 frozen bananas
2. Complete the following sentence to explain the meaning of #1:
In order to make a profit, I have to sell a minimum of________

Answer:

1. C(n) = 2.25n + 120

2. R(n) = 3.51n

3. P(n) = 1.26n - 120

1. 96 frozen bananas must be sold in order to make a positive profit.

2. In order to make a profit, I have to sell a minimum of 96 frozen bananas.

Step-by-step explanation:

1. Write a function, C(n), to represent your total costs for the week if you sell n frozen bananas.

Total cost is the addition of total variable cost and total fixed cost. Therefore, the function is as follows:

C(n) = 2.25n + 120

Where 2.25n is the total variable cost while 120 is the total fixed cost.

2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week.

Revenue is equal to selling price per unit multiplied by the number of units sold. Therefore, the function is as follows:

R(n) = 3.51 * n

R(n) = 3.51n

Where 3.51 is the selling price per unit while n the number of units sold.

3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week.

Profit is equal to total revenue minus total cost. Therefore, the function can be derived as follows:

P(n) = R(n) - C(n)

P(n) = 3.51n - 2.25n + 120

P(n) = 1.26n - 120

1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number.

This can be obtained by equating the profit function to zero and solve for n as follows:

P(n) = 0 => 1.26n - 120 = 0

Therefore, we have:

1.26n = 120

n = 120 / 1.26

n = 95.2380952380952 frozen bananas

Writing it as a whole number, we have:

n = 95 frozen bananas

However, using this whole number will result in a negative profit by substituting it into the profit function as follows:

P(n) = (1.26 * 95) - 120 = -$0.30

Therefore, n has to be increased by one to 96 which is also a whole number to have a positive profit as follows:

P(n) = (1.26 * 96) - 120 = $0.96

Therefore, 96 frozen bananas must be sold in order to make a positive profit.

2. Complete the following sentence to explain the meaning of #1:

In order to make a profit, I have to sell a minimum of 96 frozen bananas.

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