The​ Farm-4-Less tractor company produces a grain combine​ (GC) in addition to both a large​ (LT) and small size tractor​ (SM). Its production manager desires to produce to customer demand using a mixed model production line. The current sequence of​ production, which is repeated 24

times during a​ shift, is:
SM
​-GC​-SM​-LT​-SM​-LTdashSMdashGCdashSMdashLT
A new machine is produced every 2

minutes. The plant operates two​ eight-hour shifts. There is no downtime because the​ four-hours between each shift are dedicated to maintenance and restocking raw material. Based on this​ information, answer the following questions.
Part 2
a. How long does it take the production cycle to be​ completed?
The cycle sequence is completed in enter your response here

minutes. ​(Enter your response as a whole​ number.)
Part 3
b. How many of each type of machine does​ Farm-4-Less produce in a​ shift? ​(Enter your responses as whole​ numbers.)
Type

Quantity in a shift
SM

enter your response here
LT

enter your response here
GC

enter your response here

**Part 2: Production Cycle Duration**  
To find the length of the cycle, let’s analyze the given sequence:

The sequence is: **SM-GC-SM-LT-SM-LT-SM-GC-SM-LT**

Since each machine is produced every 2 minutes, we need to count the total number of machines in one complete cycle:

1. The sequence consists of 6 **SM**, 3 **LT**, and 2 **GC**.

Adding them up, we have a total of \( 6 + 3 + 2 = 11 \) machines produced in one cycle.

The total time for one cycle is:  
\[
11 \text{ machines} \times 2 \text{ minutes per machine} = 22 \text{ minutes}
\]

Therefore, the production cycle is completed in **22 minutes**.

**Part 3: Quantity Produced in a Shift**  
The plant operates two 8-hour shifts. In one shift, the total time is:
\[
8 \text{ hours} \times 60 \text{ minutes per hour} = 480 \text{ minutes}
\]

To find the number of cycles completed in one shift:
\[
\text{Number of cycles per shift} = \frac{480 \text{ minutes}}{22 \text{ minutes per cycle}} = 21.82
\]

Since the number of cycles must be a whole number, we round down to 21 complete cycles in a shift. Now, let’s calculate the number of each machine type produced in one shift:

1. **SM in one cycle:** 6  
   **SM in one shift:** \( 21 \text{ cycles} \times 6 = 126 \)

2. **LT in one cycle:** 3  
   **LT in one shift:** \( 21 \text{ cycles} \times 3 = 63 \)

3. **GC in one cycle:** 2  
   **GC in one shift:** \( 21 \text{ cycles} \times 2 = 42 \)

### Final Answer:
- **SM:** 126
- **LT:** 63
- **GC:** 42

Would you like more details or have any questions about this calculation? Here are some follow-up questions to help you dive deeper:

1. What impact would adding downtime between shifts have on total production?
2. How would a change in production cycle (e.g., producing more LT or GC) affect the overall output?
3. What if a machine took longer than 2 minutes to produce—how would this affect the cycle duration?
4. How many total machines are produced in a full day (including both shifts)?
5. What would happen to production counts if the shifts were extended to 10 hours?

**Tip:** When calculating production cycles, always verify the number of machines per cycle to avoid miscounts.

The Farm-4-Less tractor company produces a grain combine (GC) in addition to both a large (LT) and small size tractor (SM). Its production manager desires to produce to customer demand using a mixed model production line. The current sequence of production, which is repeated 24 times during a shift, is: SM-GC-SM-LT-SM-LT-SM-GC-SM-LT. A new machine is produced every 2 minutes. The plant operates two eight-hour shifts. There is no downtime because the four hours between each shift are dedicated to maintenance and restocking raw material. Based on this information, answer the following questions. Part 2: a. How long does it take the production cycle to be completed? Part 3: b. How many of each type of machine does Farm-4-Less produce in a shift?

Learn how to calculate the production cycle duration and machine output for the Farm-4-Less tractor company. This example demonstrates time and rate calculations, with a step-by-step solution to determine cycle completion time and total production per shift. Suitable for high school math students.

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