Question

How many computers must the AB Computer Company sell to break even? Let x be the number of computers.

Answer 1

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:

$c(x)=145+\frac{1}{4}x$

$r(x)=1.5x$

$145+\frac{1}{4}x=1.5x$

$145+0.25x=1.5x$

$1.5x=145+0.25x$

$1.5x-0.25x=145+0.25x-0.25x$

$1.25x=145$

$\frac{1.25x}{1.25}=\frac{145}{1.25}$

$x=116$

Therefore, the AB Computer Company must sell 116 computers to break-even.

Answer 2

Answer: $10\ computers$

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:

$c(x)=145+\frac{1}{4}x$

And given the Revenue function:

$r(x)=15x$

We must equate them:

$c(x)=r(x)\\\\145+\frac{1}{4}x=15x$

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:

$145+\frac{1}{4}x=15x\\\\145=15x-\frac{1}{4}x\\\\145=14.75x\\\\x=9.83\\\\x\approx10$

Therefore, the AB Computer Company must sell 10 computers to break even.