Question

4. The cost for implementing a manufacturing process that has a capacity of 6000 units per day was $275,000. If the cost for a plant with a capacity of 100,000 units per day was $1.5 million, what is the value of the exponent in the cost-capacity equation?

Answer 1

Cost capacity equation :

With an exponent of 0.6, doubling the capacity of a plant increases costs by approximately 50 percent, and tripling the capacity of a plant increases costs by approximately 100 percent.

The general equation for updating costs through the use of a cost index is:

   C_t = C_o (I_t)   / I_o   

   where C_t = estimated cost at present time t

C_o = cost at previous time t_o

I_t = Index value at time t

I_o = Index value at time t_o

This cost capacity equation is often called the sisth-tenths rule or the seventh-tenths rule because the exponent n, has an approximate value of 0.6-0.7 for many types of plant and machinery.

by solving through this equation we can get the eponent value .