Suad Alwan, the purchasing agent for Dubai Airlines, has found that the third pl
ID: 2746372 • Letter: S
Question
Suad Alwan, the purchasing agent for Dubai Airlines, has found that the third plane it needed from a Brazilian manufacturer took that firm 20,000 hours to produce. Using an 75% learning curve and a $40 per hour labor charge, Suad wishes to calculate what thirteen additional planes should cost
Time required for the 11th unit =
Cost of the 11th unit =
Time required for the 12th unit=
Cost of the 12th unit =
Time required for teh 13th unit
Cost of the 13th unit =
Time required for teh 14th unit=
Cost of the 14th unit =
The combinded time for the four planes = hours
The combinded cost for the four planes = dollars
Explanation / Answer
Tn = T1 * n^b
where,
Tn = time required to complete the nth unit
T1 = time required to complete the 1st unit
b = ln (learning percentage/100) / ln (2)
also Cn = cost for producing nth unit = Tn * 40
So, using this formula
T3 = T1 * 3^(ln0.75/ln2)
i.e. 20,000 = T1 * 3^(-0.415037) = T1* 0.6338
therefore T1 = 31553.89 hours, time required to produce the 1st unit
Using T1, we can compute
T11 = T1 * 11^(-0.415037) = 31553.89 * 0.3696 = 11663.7
C11 = 11663.7 * 40 = $ 466548
T12 = T1* 12^(-0.415037) = 31553.89 * 0.3565 = 11250
C12 = 11250 * 40 = $ 450000
T13 = T1* 13^(-0.415037) = 31553.89 * 0.3448 = 10882.4
C13 = 10882.4 * 40 = $ 435296
T14 = T1* 14^ (-0.415037) = 31553.89 * 0.3344 = 10552.79
C14 = 10552.79 * 40 = $ 422111.67
Combined time for the four planes = 44,348.89 hours
Combined cost for the four planes = $ 17,73,955.67