Answer :
In this scenario, since there are no fixed costs, the company would reach the break-even point at zero units. This means that the company would start generating a profit with the very first gear produced and sold.
The NC lathe problem involves analyzing the break-even point for producing a gear using an NC lathe. The gear has a selling price of $150, and the cost of production on the NC lathe is $75.
To calculate the break-even point, we need to determine the quantity of gears that must be produced and sold to cover the total costs. The total costs consist of both variable costs (costs that vary with the number of units produced) and fixed costs (costs that remain constant regardless of production volume).
Let's assume there are no fixed costs associated with the production of the gears. In this case, the break-even point can be calculated using the following formula:
Break-even point = Total fixed costs / Contribution margin per unit
Since there are no fixed costs, the contribution margin per unit is equal to the selling price minus the variable cost per unit:
Contribution margin per unit = Selling price - Variable cost per unit
= $150 - $75
= $75
By substituting these values into the formula, we can determine the break-even point:
Break-even point = 0 / $75
= 0 units
In this scenario, since there are no fixed costs, the company would reach the break-even point at zero units. This means that the company would start generating a profit with the very first gear produced and sold.
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