A machine cell consumes 200 pounds of material daily. Material is transported in 20-pound vats. The cycle time for the vats is approximately two hours. The manager has assigned an inefficiency factor of 0.08 to the cell. The plant operates for eight hours a day. How many vats are needed?

To calculate the number of vats needed for the machine cell, we need to consider the daily material consumption, the capacity of each vat, the inefficiency factor, and the plant operating hours.

1. Calculate the basic number of vats needed without the inefficiency factor: - The cell consumes 200 pounds of material daily. - Each vat can transport 20 pounds of material.

So, the number of vats needed per day without inefficiency factor would be: 200 pounds / 20 pounds per vat = 10 vats

2. Adjust for the inefficiency factor: - The inefficiency factor assigned is 0.08 (which is 8%). - This means that the actual number of vats needed should be increased by 8% to account for inefficiencies.

Adjusted number of vats = Basic number of vats needed + (Basic number of vats needed * inefficiency factor) Adjusted number of vats = 10 vats + (10 vats * 0.08) Adjusted number of vats = 10 vats + 0.8 vats Adjusted number of vats = 10.8 vats

Since we cannot have a fraction of a vat, we round up to the nearest whole number: Adjusted number of vats = 11 vats

3. Consider the cycle time and operating hours: - The cycle time for the vats is two hours. - The plant operates for eight hours a day.

Since one vat is used for two hours before it is available again, over the course of an eight-hour day, one vat can be used four times (8 hours / 2 hours per cycle = 4 cycles).

4. Determine the final number of vats needed: Although the initial calculation suggests that 11 vats would be needed to cover the entire day's operation, the cycle time allows each vat to be used multiple times during the day. Therefore, due to the cycling of vats, and assuming the material usage is evenly spread throughout the day, the same 11 vats can be reused across the eight operating hours.

Given that a vat can be used four times a day, the initial calculation of 11 vats is indeed sufficient to meet the daily demand, considering the vat's two-hour cycle time and plant's eight-hour operating schedule.

So, the plant would need 11 vats to meet its daily material consumption needs, taking into account the inefficiency factor and operational constraints.