If unit 1 requires 200 hours to produce and the labor records for an Air Force contract of 50 units indicates an average labor content of 63.1 hours per unit, what was the learning rate? What total additional 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 contracts, and hence the bidding process in general?

Answer is explained in the explanation section below.

Explanation:

Solution:

We are given that, it takes 200 hours to produce unit 1.

And we also know that the average time taken to produce the first 50 units, it takes 63.1 hours per unit.

Total Time Taken for first 50 units will be:

63.1 x 50 = 3,155 hours.

Now, if we calculate the cumulative time taken to produce first 50 units with respect to time taken to unit 1, we get:

= 15.78

So, now we can check the learning rate from the cumulative learning curve values table for 50 units and corresponding 15.78 value, we get 75%.

So, Learning rate is 75% for first 50 units production.

Now, for the second contract, total number of units to be produced are 100 units. So, again, with the help of cumulative learning curve values table, we can check the amount of cumulative time taken with respect to the production time of first unit against the learning rate of 75%.

Check the 100 units value in the 75% column, we get  24.18

So, now we can calculate the total time taken to produce 100 units:

24.18 x 100 = 4836 hours.

Now, the extra time required for the second 50 units production is the difference between the total time of 100 units and first 50 units.

4836 - 3155 = 1681 hours

From this value, we can calculate the average amount labor content per unit taken for the second contract.

1681/50 = 33.62 hours/unit.

And Combined Average amount of both contracts will be:

4836/100 = 48.36 hours/unit.

Cost Calculation:

With the help of above values, we can calculate the total cost of both the projects.

Second Contract Total cost = 1681 x $10 = $16810

Similarly for Contract one = 3155 x $10 = $31,550

Now,

Profit from the Second Contract:

($550 x 50) - $16,810 = $10,690

Similarly, for the first contract:

 ($550 x 50) - $31,550 = -$4,050 (Loss)

Hence, we can see the profits from the second contract is higher and it is feasible to fix the labor cost of first contract at:

= $8.71/hr to escape from the losses of the first contract.

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