An entrepreneur considers three possibilities for the production of her new product. One alternative, a job process, would have fixed costs of $22,000 and a per unit cost of $11.63

Question

The large batch option would have a fixed cost of $54,000 and a per unit cost of $8.82. The line process would have a fixed cost of $85,000 and a per unit cost of $7.33. Graph the total cost lines and determine over what range of output each production alternative is superior.

Answer 1

The Line alternative total cost line has the equation 85000 + 7.33x
The Large Batch alternative total cost line equation is 54000 + 8.82x
The Job alternative total cost line equation is 22000 + 11.63x

We know that the alternative with the lowest fixed cost must initially be superior and the alternative with the lowest variable cost must ultimately be the cheapest alternative, so our answer begins at 0 output with Job and ends at infinity (or at least very large output with Line).

At a volume of 11,388 the Job process becomes more expensive than the Large Batch process.
54,000 + 8.82x = 22,000 + 11.63x
32,000 = 2.81x
x = 11,388

At a volume of 20,805 the Line process becomes less expensive than the Large Batch process.
85,000 + 7.33x = 54,000 + 8.82x
31,000 = 1.49x
x = 20,805

The Line and Job processes' point of indifference is immaterial since the Large Batch process cost is lower than both at their intersection point.

The ranges for each alternative are:
Job 0 - 11,388 units
Large Batch 11,388 - 20,805 units
Line 20,805 - infinite demand