This is 80 × 2 × 2 × .8. This is incorrect for three reasons. (1) 80 is the number of units manufactured in the first order. It is not the number of hours of direct labor required to manufacture those 80 units, and the number of hours of direct labor is what should be used. (2) One multiplication by .8 is missing in the calculation. The number of hours required for the first order of 80 units should be multiplied by 2 × .8 × 2 × .8 to find the number of hours required for units 1 through 320. But that number of hours is still not the answer to the problem. (3) The number of hours required for the first 80 units needs to be subtracted from the number of hours calculated in (2) to find the number of hours required for only units 81 through 320, because those units represent the new order for 240 units.
This answer does not take into consideration the learning curve and the improvements that come with it. This is the number of direct labor hours that would be required to manufacture 240 units if no learning at all took place. See the correct answer for a complete explanation.
With an 80% learning curve it means that each time production doubles, the number of hours required for the new production will be 80% less than would be expected given previous production. Therefore, producing a total of 160 units will take 192 hours (120 × 2 × .8). Based on the fact that the first 80 units took 120 hours, we would expect that production of 160 units would take 240 hours. However, it took only 80% of that time, or 192 hours. Given that 160 units take 192 hours, we would expect that 320 units would take 384 hours. However, it will take only 80% of that time because of the learning curve. This means it will take only 307.2 hours to produce 320 units. Since the question is how many hours will be needed to produce the additional 240 units, we need to subtract the time to produce the first 80 units (120 hours) from the time required to produce all 320 units (307.2 hours). This means that it will take 187.2 hours to produce the additional 240 units.
This is the amount of time it will take to produce 320 units, not the amount of time it will take to produce the additional 240 units. Since the question asks how many hours will be needed to produce the additional 240 units, we need to subtract the time required to produce the first 80 units from the time required to produce all 320 units.
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