A supervisor needs to produce metal nameplates for bicycles. Two machines are available. The first requires a single die that costs $600. The plates will take 3 minutes each to produce at a total cost of $60 an hour. The second machine requires no initial expense but takes 6 minutes to produce at a total cost of $60 an hour. Calculate the break-even point

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To calculate the break-even point, we need to determine the production volume at which the costs for both machines are equal. In other words, we want to find the point where the cost of using the first machine (with the die) is the same as the cost of using the second machine (with no initial expense).

Let's start by calculating the cost per unit for each machine.

For the first machine:
- The cost of the die is $600, which is a one-time expense.
- The production time per unit is 3 minutes, which is 3/60 = 0.05 hours.
- The machine cost is $60 per hour.

So, the cost per unit for the first machine is:
$600 (die cost) + ($60/hour * 0.05 hours) = $600 + $3 = $603.

For the second machine:
- There is no initial expense.
- The production time per unit is 6 minutes, which is 6/60 = 0.10 hours.
- The machine cost is $60 per hour.

So, the cost per unit for the second machine is:
$60/hour * 0.10 hours = $6.

To find the break-even point, we need to equate the costs for both machines.

Let's assume the break-even point is x units.

For the first machine, the total cost would be:
x units * $603 per unit = $603x.

For the second machine, the total cost would be:
x units * $6 per unit = $6x.

Setting these two costs equal to each other, we have:
$603x = $6x.

To solve for x, we can divide both sides of the equation by $6:
$603x / $6 = $6x / $6,
$100.50x = x.

This equation tells us that the production volume x is equal to 1.

Therefore, the break-even point is reached at 1 unit of production.