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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**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.
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
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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