Question

For an assembly line, the inventory was calculated by considering the production rate as 4 pieces per hour and the average processing time as 60 minutes. Now, if the production rate is kept the same and the average processing time is brought down by 30%, then the change in inventory is

• A. Decreased by 25%
• B. Increased by 25%
• C. Decreased by 30%
• D. Increased by 30%

Hint:

Since $I = R \times T$, if the production rate ($R$) is kept entirely constant, the inventory ($I$) becomes directly proportional to the processing time ($T$): \[ I \propto T \] Therefore, whatever percentage change happens to the processing time will directly map onto the inventory level! A 30

Answer 1

The Correct Option is C

Step 1: Set up the proportional relationship.
By Little's law, inventory \( I = R \times T \), where \( R \) is the production rate and \( T \) is the processing time. Since the production rate \( R \) is not changing in this problem, inventory is directly proportional to the processing time alone, so any percentage change in \( T \) shows up as the same percentage change in \( I \).

Step 2: Apply the 30% cut in processing time.
The processing time is brought down by 30%, so \( T_2 = 0.7\,T_1 \). Because \( I \) is proportional to \( T \) at constant \( R \), \( I_2 = 0.7\,I_1 \), which means the inventory also falls by exactly 30%. \[ \boxed{\text{Inventory decreases by } 30\%} \]