Answer :
At noon, there are 20,000 gallons of milk in the queue to be processed.
To find out how many gallons of milk are in the queue to be processed at noon, we first need to calculate how many gallons of milk have been processed by noon.
The company can process milk at a fixed rate of 7500 gallons per hour. From 8 a.m. to noon, there are 4 hours.
Total gallons processed by noon = Rate of processing Time
[tex]\[ = 7500 \, \text{gallons/hour} \times 4 \, \text{hours} = 30000 \, \text{gallons} \][/tex]
Now, we need to find out how many gallons of milk are still in demand by noon. The total demand over the course of the day is 100,000 gallons, and it is spread out uniformly from 8 a.m. to 6 p.m.
This means that by noon, half of the day has passed.
So, the total demand by noon = Total demand / 2
[tex]\[ = \frac{100000}{2} = 50000 \, \text{gallons} \][/tex]
Now, to find out how many gallons are in the queue to be processed at noon, we subtract the gallons already processed from the total demand:
Gallons in the queue at noon = Total demand by noon - Gallons processed by noon
[tex]\[ = 50000 \, \text{gallons} - 30000 \, \text{gallons} = 20000 \, \text{gallons} \][/tex]
So, at noon, there are 20,000 gallons of milk in the queue to be processed.
Final answer:
At noon, the Shady Farm Milk Company has 10,000 gallons of milk in the queue to be processed given the demand and the processing rate.
Explanation:
The Shady Farm Milk Company can process 7500 gallons of milk per hour. Given that the company operates from 8 a.m. to 6 p.m., this is a total of 10 hours of operation in a day. Therefore, in 10 hours, the company can process 7500 × 10 = 75,000 gallons of milk.
However, the demand for milk is 100,000 gallons over the course of the day. Therefore, by noon, the company has been operating for 4 hours, meaning they can process 7500 × 4 = 30,000 gallons.
The demand over the same 4 hours period (from 8 a.m. to noon) is calculated by dividing the total demand over the entire course of the day (which is evenly spread) by the number of operating hours. Thus: 100,000 / 10 = 10,000 gallons/hour.
Consequently, the demand from 8 a.m. to noon is: 10,000 × 4 = 40,000 gallons. So, the amount of milk in the queue at noon would be the demand minus what the company has processed at that time.
Hence: 40,000 (demand from 8 a.m. to noon) - 30,000 (processed milk from 8 a.m. to noon) = 10,000 gallons. Therefore, at noon, the company has 10,000 gallons of milk in the queue to be processed.
Learn more about Queue here:
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