Question

Mass Balance Company is manufacturing a new digital scale for use by large chemical companies has come up with a marketing hit. The original production run was for 400 units and these have been produced and shipped. Now, marketing has forecast a demand for an additional 200 units (“if the price is right”). The first scale took 125 hours of direct labor and the second took 110 hours to complete. Per Adam Smith and his academic descendant Professor Culp we will assume the product’s price contains the components material, labor, overhead, and profit at $150/labor hour expended.

1. What is the learning rate?
2. What is the estimated time for the 600th unit?
3. What was the estimated total time for producing the first 400 units?
4. What was the average selling price for the first 400 units?
5. What could be the average selling price for the next 200 units?
6. What kind of price discount would you recommend to marketing for the next 200 units under consideration?

USING EXCEL

Answer 1

a)

Direct labor to produce first unit, T1 = 125 hours

Direct labor to produce second unit, T2 = 110 hours

Learning rate, r = T2/T1 = 110/125

= 0.88

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b)

Estimated time for the 600th unit, T600

= T1*r^{ln(600)/ln(2)}

= 125*0.88^9.22882

= 38.42 hours

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c)

Estimated total time to produce the first 400 units is determined by Crawford's formula as shown below

EXCEL FORMULA:

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d)

Total direct labor hours for the first 400 units = 20239.51 hours

Average direct labor hours per unit = 20239.51/400

= 50.6 hours

Average selling price = 50.6*150

= $ 7,590