A company is preparing a bid on a government contract for 40 units of a certain product. The operations manager estimates the assembly time required for the first two units to be 10.4 hours and 8.8 hours.What is the expected time required to produce the fortieth unit?
A)3.2 hours
B)4.4 hours
C)5.9 hours
D)3.7 hours
E)2.2 hours

Question

Quizplus · Accepted Answer

The expected time required to produce the fortieth unit can be calculated using the learning curve theory, which suggests that the time required to complete a task will decrease at a consistent rate as production increases due to learning and efficiency improvements. The formula to calculate the time for the nth unit is Tn = T1 * n^b, where T1 is the time to produce the first unit, n is the unit number, and b is the learning rate coefficient calculated as b = log(learning percentage) / log(2). Given T1 = 10.4 hours and T2 = 8.8 hours, we first find the learning percentage as 8.8 / 10.4 = 0.846 (or 84.6%). Then, b = log(0.846) / log(2). To find the time for the 40th unit, we apply the formula with n = 40. The calculation will show that the time for the 40th unit aligns closest with option B, 4.4 hours, indicating significant efficiency gains through the learning curve effect.

A Company Is Preparing a Bid on a Government Contract