Question

ii) At an assembly plant, managers use a progress ratio of 0.8. Currently, workers have assembled 100,000 units of the product and the variable cost per unit is $500. What is the expected variable cost per unit for the 400,000th product assembled? Why?

Answer 1

C=C0(X^b)

C=Average Cost  per unit

C0=Cost to  produce the first piece

X=Cumulative units of production

b=Learning Index

For Progress Ratio=0.8

b=Log 0.8/Log2=-0.322

Progress Ratio=0.8

Average Cost per unit is reduced by 20% as cumulative production doubles

At cumulative quantity =200,000(100000*2)

Variable Cost per unit =Progress Ratio*($500)=0.8*500=$400

At cumulative quantity =400,000(200000*2)

Variable Cost per unit =Progress Ratio*($400)=0.8*400=$320

If you use the formula:

C=C0(X^b)

C=Average Cost  per unit

C0=Cost to  produce the first piece

X=Cumulative units of production

b=Learning Index

For Progress Ratio=0.8

b=Log 0.8/Log2=-0.322

When X=100000

C=$500=C0*(100000^-0.322)

C0=500/(100000^-0.322)

When, X=400000

C=Average Cost per unit=C0*(400000^-0.322)=(500/(100000^-0.322))*(400000^-0.322)=500*0.64=$320

ANSWER: $320