Question

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

Cost Function: C (x) = 145 + 1/4x
Revenue Function: R (x) = 1.5x

Answer 1

AB Computer Company must sell 116 computers to break even.

Explanation:

1. Let's check the information given to resolve the case:

Cost Function: C (x) = 145 + 1/4x

Revenue Function: R (x) = 1.5x

Break even is the point in which total cost and total revenue are equal

2. Let's use this formula to find out the break even point and the number of computers necessary to sell:

Revenue - Cost = 0

1.5x - (145 + 1/4x) = 0

1.5x - 145 - 0.25x = 0 (1/4 = 0.25)

1.25x - 145 = 0

1.25x = 145 (Adding 145 to both sides of the equation)

x = 145/1.25 (Dividing by 1.25 at both sides)

x = 116

AB Computer Company must sell 116 computers to break even.

Answer 2

The Company AB must sell 116 computers to break even

Explanation:

we have

`R(x)=1.5x` -----> equation A

`C(x)=145+(1)/(4)x` ----> equation B

where

C is the cost function

R is the revenue function

x is the number of computers sold

we know that

Break even is when the cost is equal to the revenue

so

equate equation A and equation B

`1.5x=145+(1)/(4)x`

Solve for x

subtract 1/4x both sides

`1.5x-(1)/(4)x=145\\1.5x-0.25x=145\\1.25x=145`

Divide by 1.25 both sides

`x=116`

therefore

The Company AB must sell 116 computers to break even