Final answer:
The approximate cost of the new larger centrifuge with a capacity of 4500 gallons per hour, considering the cost index change from 120 to 300 and an exponent of 0.75, is $227,950.
Step-by-step explanation:
To calculate the current cost of a new centrifuge, we'll use the cost-capacity factor which incorporates the power-sizing exponent. The formula for scaling the cost of industrial equipment as capacity changes is given by:
C2 = C1 (Q2/Q1)^x
Where:
C2 is the new costC1 is the original costQ2 is the new capacityQ1 is the original capacityx is the power-sizing exponent
In this case:
C1 = $40,000Q1 = 1500 gallons/hourQ2 = 4500 gallons/hourx = 0.75
First, calculate C2 based on capacity change:
C2 = $40,000 * (4500/1500)^0.75
Next, adjust for the change in cost index from 120 to 300:
Adjusted C2 = C2 * (Current Cost Index / Previous Cost Index)
Adjusted C2 = $40,000 * (3)^0.75 * (300 / 120)
Finally, compute the cost:
Adjusted C2 = $40,000 * 30.75 * 2.5 = $227,950
Thus, the approximate cost in today's dollars of the new larger centrifuge is $227,950, which corresponds to option (c).