Question

Five years ago, when the relevant cost index was 120, a nuclear centrifuge cost $40,000. The centrifuge had a capacity of separating 1500 gallons of ionized solution per hour. Today, it is desired to build a new centrifuge with capacity of 4500 gallons per hour, but the cost index now is 300. Assuming a power sizing exponent to reflect economies of scale, x, of 0.75, use the power sizing model to determine the approximate cost (expressed in today's dollars) of the new reactor.

Answer 1

The approximate cost (expressed in today's dollars) of the new reactor is $227,950.71.

Step-by-step explanation:

This can be calculated as follows:

Cost of centrifuge with 4500 capacities 5 years ago / Cost of centrifuge with 1500 capacities 5 years ago = (Capacity of centrifuge with 4500 capacities / Capacity of centrifuge with 1500 capacities)^Power sizing exponent

Cost of centrifuge with 4500 capacity 5 years ago / $40,000 = (4500 / 1500)^0.75

Cost of centrifuge with 4500 capacities 5 years ago / $40,000 = 2.27950705695478

Cost of centrifuge with 4500 capacities 5 years ago = 2.27950705695478 * $40,000 = $91,180.28

Therefore, we have:

Cost of centrifuge with 4500 capacities now = (Cost index now / Cost index 5 years ago) * Cost of centrifuge with 4500 capacities 5 years ago = (300 / 120) * $91,180.28 = $227,950.71

Therefore, the approximate cost (expressed in today's dollars) of the new reactor is $227,950.71.