Answer:
a. Capacity = 33.64 kg/hour
b. Utilization = 70.09%
c. Average inventory = 19.79 kg
d. The desired Batch size = 106 kg
e. 17.77 kg of Fragola must be produced.
Explanation:
For part a:
We have the formula of Batch size:
Batch size = (Capacity x Setup time)/(1 - Capacity x Processing time)
Here, we have:
Setup time = 3/4 hours + 1/3 hours + 1/4 hours = 4/3 hours
Batch size = 150 kg
Processing time = 1/48 hr/kg
Solve for Capacity now,
Capacity = 33.64 kg/hour
For Part B:
We have the formula of Utilization as:
Utilization = Actual capacity / Designed capacity
Utilization = 33.64/48 x 100 = 70.09%
Utilization = 70.09%
For part C:
We know that, The Flow Rate of chocolato is 10 kgs/hr
And The processing time of chocolato is 1/48 hr / kg
And Chocolato is 1/3 of total demand, so the batch size for chocolato is 1/3 x 150 = 50 kgs.
Formula for Average inventory is:
Average inventory = (1/2) x Batch size x (1- Flow rate x Processing
time)
Average inventory = 0.5 x 50 x (1 – 10 x 1/48 )
Average inventory = 19.79 kg
For part d:
We already know the formula for Batch size. So,
Batch size = (Capacity x Setup time)/(1- Capacity x Processing time)
Each batch consists of three flavors, so:
We know the following data as well:
Setup time = 3/4 hours + 1/3 hours + 1/4 hours = 4/3 hours
Desired Capacity = 5 kg + 10 kg + 15 kg = 30 kg
Processing time = 1/48 hr/kg
Hence,
The desired batch size = (30 x 4/3)/(1 - (30 x 1/48)) = 106 kg
The desired Batch size = 106 kg
For Part e:
Fragola is 5/30 of the total demand, so produce:
(5 kg/30 kg)/(106 kg) = 17.77 kg
17.77 kg of Fragola must be produced.