Youve just completed a pilot run of 10 units of a major prod

You’ve just completed a pilot run of 10 units of a major product and found the processing time for each unit was as follows: UNIT: NUMBER TIME (HOURS) 1:810 2:620 3:570 4:500 5:480 6:460 7:440 8:420 9 :395 10:380 a. According to the pilot run, what would you estimate the learning rate to be? (Do not round intermediate calculations. Round your answer to the nearest whole percent.) b. Based on (a), how much time would it take for the next 190 units, assuming no loss of learning? (Round your answer to the nearest whole number.) c. How much time would it take to make the 1,000th unit? (Round your answer to the nearest whole number.)

Solution

(a) T1= 810, T2= 620, T3=570, T4=500, T5= 480, T6= 460, T7= 440, T8= 420, T9= 395, T10= 380

Learning rate is based on doubling of production and can be calculated when units are doubled.

ie. Learning rate= T2/T1 or T4/T2 or T6/T3 or T8/T4 of T10/T5

T2/T1= 620/800= 0.775= 77.5 %

T4/T2= 500/620= 0.806= 80.6 %

T6/T3= 460/570= 0.807= 80.7 %

T8/T4= 420/500= 0.84= 84 %

T10/T5= 380/480= 0.791= 79.1 %

If we average out the above, the Learning rate comes out to be approx 80%

(b) For calculating total time required for the next 190 units, the formula to be used is:

Time taken to produce first 10 units= 810+620+570+500+480+460+440+420+395+380=5075 hours

If the Total time required to make 200 units is calculated, Time taken to produce first 10 units may be subtracted from it get the Total time required to make next 190 units.

Average time per unit for 200 units= T1 x 200^ (Log(Learning rate)/Log 2)= 810 x 200^ (-0.322)= 147 hours

Therefore, Total time to produce 200 units= 200 x 147= 29400 hours

Hence, time required to make next 190 units= 29400-5075= 24325 hours

(c) Tn= T1 n^b

where b= Log(Learning rate)/Log 2= Log(0.80)/Log 2= -0.322

Therefore, T1000= 810 x (1000^(-0.322))= 87.59 hours

Hence, time to make 1000th unit is approx 88 hours