Answer: [tex]10\ computers[/tex]
Step-by-step explanation:
To solve this exercise it is important to remember the cost must be equal to the revenue in order to break even.
In this case, given the Cost function:
[tex]c(x)=145+\frac{1}{4}x[/tex]
And given the Revenue function:
[tex]r(x)=15x[/tex]
We must equate them:
[tex]c(x)=r(x)\\\\145+\frac{1}{4}x=15x[/tex]
Since "x" represents the number of computers that AB Computer Company must sell to break even, we have to solve for "x" in order to find its value.
Then:
[tex]145+\frac{1}{4}x=15x\\\\145=15x-\frac{1}{4}x\\\\145=14.75x\\\\x=9.83\\\\x\approx10[/tex]
Therefore, the AB Computer Company must sell 10 computers to break even.
Answer:
116 computers.
Step-by-step explanation:
We have been given cost function and revenue function for AB Computer Company. We are asked to find the break-even point.
We know that break-even is a point, when total cost is equal to total revenue that is company make no profit or no loss.
To find break-even, we will equate cost function with revenue function and solve for x as:
[tex]c(x)=145+\frac{1}{4}x[/tex]
[tex]r(x)=1.5x[/tex]
[tex]145+\frac{1}{4}x=1.5x[/tex]
[tex]145+0.25x=1.5x[/tex]
[tex]1.5x=145+0.25x[/tex]
[tex]1.5x-0.25x=145+0.25x-0.25x[/tex]
[tex]1.25x=145[/tex]
[tex]\frac{1.25x}{1.25}=\frac{145}{1.25}[/tex]
[tex]x=116[/tex]
Therefore, the AB Computer Company must sell 116 computers to break-even.
