Question

The manufacturer of an energy drink spends $1.40 to make each drink and sells them for $3. The manufactureralso has fixed costs each month of $10000.a. Find the cost function C when x energy drinks are manufactured.C(x) =Previewb. Find the revenue function R when x drinks are sold.R(2) =Previewc. Find the break-even point by any method.drinks2 =

Answer 1

C(x) = 10000 + 1.4x

R(x) = 3x

x = 6250 drinks

Step-by-step explanation

Given that:

The cost of producing an x drink = $1.40

The fixed costs each month = $10, 000

The selling price of each drink = $3

To find the cost function, revenue function, follow the steps below

For every x drinks manufactured, the company spends $1.4

Step 1: Write the general formula for calculating the cost function

`\text{ C\lparen x\rparen = F + V\lparen x\rparen}`

Where F is the fixed cost, and V is the variable cost

Hence, the cost function can be written below as

Recall, that the fixed cost is $10, 000

`\text{ C\lparen x\rparen = 10000 + 1.4x}`

Step 2: Write the revenue function

The general revenue function is given below as

`\text{ y = bx}`

Where

y is the total revenue function

b is the selling price per unit of sales

x is the number of units sold

Since the selling price per unit of sales is $3, hence the revenue function is written below as

`\text{ R\lparen x\rparen = 3x}`

Step 3: Find the number of drinks at the break-even point

At break-even, the cost function = the revenue function

`\begin{gathered} \text{ C\lparen x\rparen = R\lparen x\rparen} \\ \text{ 10000+ 1.4x = 3x} \\ \text{ Subtract 1.4x from both sides of the equation} \\ \text{ 10000 + 1.4x - 1.4x = 3x - 1.4x} \\ \text{ 10000 = 1.6x} \\ \text{ Divide both sides of the eqation by 1.6} \\ \text{ }(10000)/(1.6)\text{ = }(1.6x)/(1.6) \\ \text{ x = 6250 drinks} \end{gathered}`

Hence, the total number of drinks manufactured is 6250 drinks