Single: What is the incremental cost

Suppose you currently run one shift at your plant. You have $1,000 per day in administrative overhead and the daily wages and materials cost of operating the shift are $30,000.

If you expand to two shifts, your average cost per-shift per-day becomes $22000. What is the incremental cost of the new shift?

Answer

This one is all about definitions.

No matter how man shifts you have the administrative costs stay the same. The first shift costs 30,000 and the question is how much is the extra cost of adding a shift given that you know the average cost for two shifts is 22,000. The admin cost of 1,000 the incremental cost of the first shift, 30,000, and the unknown incremental cost of the second shift is shown below.

(1)
\begin{align} \frac{1,000 +30,000 +S }{2}=22,000 \end{align}

You then just solve for S and find that the incremental cost of the shift is 13,000.

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