4 The cost for implementing a manufacturing process that has

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?

Solution

Capacity, Q1 = 6,000 units
Cost at Q1, C1 = $275,000

Capacity, Q2 = 100,000 units
Cost at Q2, C2 = $1,500,000

C2 = C1 * (Q2 / Q1)^x, where x is the exponent which represent between capacities
$1,500,000 = $275,000 * (100,000 / 6,000)^x
5.4545 = 16.667^x
ln(5.4545) = x * ln(16.667)
x = 0.60

So, the value of the exponent in the cost-capacity equation is 0.60