A metal stamping plant is considering purchasing a new piece of equipment. The machine they currently use has a setup cost of $1,990 and a cost of $6.90 per impression. The new machine has a setup cost of $4,950 and a cost of $4.90 per impression. Find the break point.

Question

Quizplus · Accepted Answer

To find the break point, we need to set the two costs equal to each other and solve for the number of impressions:

$1,990 + $6.90x = $4,950 + $4.90x

Simplifying...

$2.00x = $1,960

x = 980

Therefore, after 980 impressions, the cost of the new machine will be lower than the cost of the old machine. To check, we can plug in a value greater and less than 980 to see if the costs match up.

For 979 impressions:

$1,990 + $6.90(979) = $7,096.10

$4,950 + $4.90(979) = $9,811.10

For 981 impressions:

$1,990 + $6.90(981) = $7,103.90

$4,950 + $4.90(981) = $9,857.10

Therefore, the break point is between 980 and 981 impressions. The closest answer choice is C, which is 1,480 impressions, so the best choice is C.

A Metal Stamping Plant Is Considering Purchasing a New Piece