# 2. If unit 1 requires 200 hours to produce and the labor records for an Air Force project contract of 50 units indicates an average labor content of 63.1 hours per unit, what was the learning rate? What total addi- tional number of labor hours would be required for a follow-on Air Force contract of 50 units? What would be the average labor content of this second contract? Of both contracts combined? If labor costs the vendor \$10/hour on this second contract and the price to the Air Force is fixed at \$550 each, what can you say about the profitability of the first and second con- tracts, and hence the bidding process in general?

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The time required to produce the first unit = Y1 = 200 hours

Average time for the first 50 units = Y50 = 63.1 hours

Y50 = Y1 * 50^b

or, 50^b = Y50 / Y1 = 63.1 / 200 = 0.3155

or, b = ln(0.3155) / ln(50) = -0.2949

or, ln(r) / ln(2) = -0.2949

or, r = exp(-0.2949*ln(2)) = 0.815

So, the learning rate = 81.5%

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Average time for the first 100 units = Y100 = Y1 * 100^b = 200*(100^-0.2949) = 51.44 hours

So, total hours required for the first 100 units = 100 * 51.44 = 5,144 hours

The total time to produce the first 50 units was = 50 * Y50 = 50*63.1 = 3,155 hours

So, the follow-on 50 units will require 5,144 – 3,155 = 1,989 hours

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The average labor content for the second contract = 1989 / 50 = 39.78 hours per unit

The average labor content for both the contracts combined = 5144 / 100 = 51.44 hours per unit

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Cost of the first contract = 3155 * \$10 = \$31,550

Revenue from the first contract = \$550 * 50 = \$27,500

So, the first contract will incur a loss of 31550 – 27500 = \$4,050

Cost of the second contract = 1989 * \$10 = \$19,890

Revenue from the first contract = \$550 * 50 = \$27,500

So, the first contract will incur a profit of 27500 – 19890 = \$7,610

So, the overall profit combining the two contracts = 7610 – 4050 = \$3,560