ANSWER
C(x) = 10000 + 1.4x
R(x) = 3x
x = 6250 drinks
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
[tex]\text{ C\lparen x\rparen = F + V\lparen x\rparen}[/tex]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
[tex]\text{ C\lparen x\rparen = 10000 + 1.4x}[/tex]Step 2: Write the revenue function
The general revenue function is given below as
[tex]\text{ y = bx}[/tex]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
[tex]\text{ R\lparen x\rparen = 3x}[/tex]Step 3: Find the number of drinks at the break-even point
At break-even, the cost function = the revenue function
[tex]\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{ }\frac{10000}{1.6}\text{ = }\frac{1.6x}{1.6} \\ \text{ x = 6250 drinks} \end{gathered}[/tex]Hence, the total number of drinks manufactured is 6250 drinks
