Chapter 3 - intermediate algebra

Question

1) A metal stamping plant is considering purchasing a new piece of equipment. The machine they currently use has a setup cost of $1,475 and a cost of $4.50 per impression. The new machine has a setup cost of $3,675 and a cost of $2.90 per impression. Find the break point.

_____ impressions

Answer 1

Each of these will have an equation to calculate the cost. We have to set up these equations.

In order to understand how to set up these equations, let us look at the first process:

We are told the following:

It has a set up cost of 1475

It has a per impression cost of 4.50.

So let us see the pattern:

If there were 0 impressions, then the cost would be 1475.

If there is 1 impression, then the cost would be 1475 + 4.50(1) = 1479.5

If there are 2 impressions, then the cost would be 1475 + 4.50(2) = 1484

If there are 3 impressions, then the cost would be 1475 + 4.50(3) = 1488.5

So, from this, we get a general idea that we can calculate the total cost using the following formula:

1475 + 4.50 * (# of impressions)

The new machine formula will work the same way except we have to put in the information of the new machine:

New machine formula: 3675 + 2.90 * (# of impressions)

In order to understand the breakeven point of when the costs will equal out, we have to set these two equal and solve for # of impressions:

1475 + 4.50 * (# of impressions) = 3675 + 2.90 * (# of impressions)

Solving this gives us:

# of impressions = 1375

Answer 2

Hi Cassidy,

We need the equation that describes output for each machine. Once we have those, we can set them equal to each other and solve for x to get the breakeven point. So:

Let x be the number of impressions at breakeven.

Original Machine Equation:

1475 + 4.50x

New Machine Equation:

3675 + 2.90x

Set equal to each other:

1475 + 4.50x = 3675 + 2.90x

Subtract 2.90x on both sides to isolate:

1475 + 1.60x = 3675

Subtract 1475 on both sides:

1.60x = 3675

Divide by 1.60:

x = 1375 impressions

I hope this helps.