number of cars shipped on day n. Specify a flow di- agram and a difference equation (in standard form) that describe together the number of cars shipped as a function of number of cars produced and the history of the number of cars shipped.
number of cars shipped on day n. Specify a flow di- agram and a difference equation (in standard form) that describe together the number of cars shipped as a function of number of cars produced and the history of the number of cars shipped.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem BC:5.4**
Let \( x[n] \) represent the number of automobiles produced by a factory on a given day, \( n \). Let the inventory (total number of completed cars at the factory) at the end of day \( n \) be represented by \( q[n] \).
- Each day the factory ships \( \frac{5}{6} \) of the previous day’s inventory and holds the remaining \( \frac{1}{6} \) of the previous day’s inventory for one full day of driving tests.
- The cars being tested on day \( n \) are included in the inventory count for day \( n \).
- The day after testing, all of the tested cars are shipped.
Let \( y[n] \) represent the number of cars shipped on day \( n \).
**Task:**
Specify a flow diagram and a difference equation (in standard form) that describe together the number of cars shipped as a function of the number of cars produced and the history of the number of cars shipped.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F028a22e8-f094-478d-95cf-e0334af4f4a7%2Fe24af991-eb33-48f4-9c6a-4cf06ee63cf3%2Fpmaqpm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem BC:5.4**
Let \( x[n] \) represent the number of automobiles produced by a factory on a given day, \( n \). Let the inventory (total number of completed cars at the factory) at the end of day \( n \) be represented by \( q[n] \).
- Each day the factory ships \( \frac{5}{6} \) of the previous day’s inventory and holds the remaining \( \frac{1}{6} \) of the previous day’s inventory for one full day of driving tests.
- The cars being tested on day \( n \) are included in the inventory count for day \( n \).
- The day after testing, all of the tested cars are shipped.
Let \( y[n] \) represent the number of cars shipped on day \( n \).
**Task:**
Specify a flow diagram and a difference equation (in standard form) that describe together the number of cars shipped as a function of the number of cars produced and the history of the number of cars shipped.
Expert Solution
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Step 1: describinh equation for inventory update
let's describe the processes using difference equations:
Inventory Update:
The inventory q[n] at the end of day n is updated based on the previous day's inventory and the number of cars produced and tested as follows:
q[n] = (5/6) * q[n-1] + (1/6) * x[n-1]
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