Question

A machine to manufacture fasteners has a setup cost of $1,400 and a unit costof $0.008 for each fastener manufactured. A newer machine has a setup cost of$1,850 but a unit cost of only $0.0015 for each fastener manufactured. Find thebreak point. (Round your answer to the nearest whole unit.)

Answer 1

Given:

Setup cost of machine 1 = $1400

Unit cost = $0.008

Setup cost for machine 2 = $1850

Unit cost = $0.0015

Let's find the break point.

The break point will be when the total cost for machine 1 equals the total cost for machine 2.

Apply the slope-intercept equation:

y = mx + b

Where b is the setup cost and m is the unit cost.

We have the following:

Equation for machine 1:

y = 0.008x + 1400

Equation for machine 2:

y = 0.0015x + 1850

Now, eliminate the equivalent sides and combine the expressions:

0.008x + 1400 = 0.0015x + 1850

Move all terms containing x to the left.

0.008x - 0.0015x = 1850 - 1400

0.0065x = 450

Divide both sides of the equation by 0.0065:

`\begin{gathered} (0.0065x)/(0.0065)=(450)/(0.0065) \\ \\ x=69230.76\approx69231 \end{gathered}`

Therefore, the break point is when the number if unit is 69231 units.

ANSWER:

69231