Big John’s manufacturing currently produces its lead product on a machine that has a variable cost of 0.32 per unit and a fixed cost of $75,000. Big John is considering purchasing a new machine that will drop the variable cost to $0.28 per unit, but has a fixed cost of $150,000. Find and interpret the crossover/indifference point between the two machines.

The indifference point is 1,875,000 units.

Because the current machine has lower fixed costs, it has a lower cost from 0 units to 1,874,999. From 1,875,001 the new machine is more convenient,

Explanation:

Giving the following information:

Current machine:

Total cost= 75,000 + 0.32x

New machine:

Total cost= 150,000 + 0.28x

To find the indifference point, we need to equal the cost functions and isolate x (number of units)

75,000 + 0.32x = 150,000 + 0.28x

0.04x= 75,000

x= 1,875,000

The indifference point is 1,875,000 units.

Because the current machine has lower fixed costs, it has a lower cost from 0 units to 1,874,999. From 1,875,001 the new machine is more convenient.

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