Question

A machine to manufacture fasteners has a setup cost of $1,100 and a unit cost of $0.003 for each fastener manufactured. A newer machine has a setup cost of $1,600 but a unit cost of only $0.0025 for each fastener manufactured. Find the break point. (Round your answer to the nearest whole unit.)

Answer 1

The breakeven point for both production options is 1,000,000 fasteners

What is breakeven point?

The breakeven point in this case is the point at which the total cost incurred under both production options is the same

Total cost under option 1 is the setup cost plus the total unit cost of fasteners produced

TC=1100+0.003X

Under the second option, the total cost function based on the setup cost and the total unit cost(unit cost per fastener multiplied by the number of fasteners)

TC=1600+0.0025X

At breakeven point TC(option 1)=TC(option 2)

1100+0.003X=1600+0.0025X

collect like terms

0.003X-0.0025X=1600-1100

0.0005X=500

X=500/0.0005

X=1,000,000 fasteners

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