Question

Suad​ Alwan, the purchasing agent for Dubai​ Airlines, has determined that the third plane took 18,000 hours to produce. Using an ​85% learning curve and a $35​-per-hour labor​ charge, he wants to determine the cost of the additional planes.  

a) Time required for the fifth unit​ = ___________ hours​ (round your response to the nearest whole​ number).

b) Cost of the fifth unit = _______ dollars (round your response to the nearest whole number)

c) Time required for the sixth unit = __________ hours (round your response to the nearest whole number)

d) Cost of the sixth unit = ___________ dollars (round your response to the nearest whole number)

e) Time required for the seventh unit = _________ hours (round your response to the nearest whole number)

f) Cost of the seventh unit = ___________ dollars (round your response to the nearest whole number)

Answer 1

Learning Curve Equation = Y_X = KX^S

Where,

Y = Required average for X units/lot
K = Total time or cost required for 1st unit/lot
X =Units/lots whose average is required
S = Learning Curve Index

S = Log 0.85 ÷ Log 2 = (-0.07058107÷0.30103) = -0.2345

Average Time required for the first Four units = 18,000 hours . (4÷3)^-0.2345

Average Time required for the first Four units = 16,826 hours

Average Time required for the first Five units = 18,000 hours . (5÷3)^-0.2345

Average Time required for the first Five units = 15,968 hours

(a) Time required for the Fifth units = Total time required for first five units - Total time required for first four units

Time required for the Fifth units = (15,968 hours per unit x 5 units) - (16,826 hours per unit x 4 units)

Time required for the Fifth units = 12,536 hours (Approx)

(b) Cost of the fifth unit = 12,536 hours x $ 35 per hour

Cost of the fifth unit = $438,760 (Approx)

Average Time required for the first Six units = 18,000 hours . (6÷3)^-0.2345

Average Time required for the first Six units = 15,300 hours

(c) Time required for the Sixth units = Total time required for first six units - Total time required for first five units

Time required for the Sixth units = (15,300 hours per unit x 6 units) - (15,968 hours per unit x 5 units)

Time required for the Sixth units = 11,960 hours (Approx)

(d) Cost of the sixth unit = 11,960 hours x $ 35 per hour

Cost of the sixth unit = $418,600 (Approx)

Average Time required for the first Seven units = 18,000 hours . (7÷3)^-0.2345

Average Time required for the first Seven units = 14,757 hours

(e) Time required for the Seventh units = Total time required for first seven units - Total time required for first six units

Time required for the Seventh units = (14,757 hours per unit x 7 units) - (15,300 hours per unit x 6 units)

Time required for the Seventh units = 11,499 hours (Approx)

(f) Cost of the seventh unit = 11,499 hours x $ 35 per hour

Cost of the seventh unit = $402,465 (Approx)