Question

_{Refer to the table below. Assume that the company involved now finds that the learning rate is 70 percent. The 70 percent learning rate coefficient is -0.514573; that is b= -0.514573 in the formula Y= ax Required: Using the formula, Y= ax", compute the labor time and costs for 5, 6, and 7 units. (Round your Intermediate calculations (except for coefficient) and final answers to 2 decimal places.) Unit Produced Labor Time Required to Produce the Xth Unit i.e., the last single unit produced)1 TY Cumulative Total Time in Labor- Hours(2) Total Cost(3) Average Cost per Unit(4) $ $ 100.00 70.00 56.82 49.00 100.00 170.00 226.82 275.82 5,000.00 8,500.00 11,340.90 13,790.90 5,000.00 4.250.00 3.780.30 3.447.73 34.30 430.31 21.515.75 2.689.47}

Answer 1

For 5 units

Y= ax^b

a=100

x=5

b= -0.514573

Y=100(5)^-0.514573

Taking Log both side

LogY=Log100(5)^-0.514573

LogY=Log100 + (-0.514573)Log5       i.e Logab=Loga + Logb

LogY=2 + (-0.514573)(0.698970)

LogY=1.64032891

Y=Antilog1.64032891

Y=43.684655

Cummulative time for 5 units=5*43.684655

                                                    =218.24 hours

Total Labor Cost for 5 units=218.24*50

                                                     =$10912         

For 6 units

Y= ax^b

a=100

x=6

b= -0.514573

Y=100(6)^-0.514573

Taking Log both side

LogY=Log100(6)^-0.514573

LogY=Log100 + (-0.514573)Log6       i.e Logab=Loga + Logb

LogY=2 + (-0.514573)(0..778151)

LogY=1.599585

Y=Antilog1.599585

Y=39.77269

Cummulative time for 6 units=6*39.77269

                                                    =238.64 hours

Total Labor Cost for 6 units=238.64*50

                                                     =$11932

For 7 units

Y= ax^b

a=100

x=7

b= -0.514573

Y=100(7)^-0.514573

Taking Log both side

LogY=Log100(7)^-0.514573

LogY=Log100 + (-0.514573)Log7       i.e Logab=Loga + Logb

LogY=2 + (-0.514573)(0.845098)

LogY=1.565135

Y=Antilog1.565135

Y=36.73965

Cummulative time for 7 units=7*36.73965

                                                    =257.18 hours

Total Labor Cost for 7 units=257.18*50

                                                     =$12859