Comprehension
The table below shows the raw material requirement (in units) for a crank-shaft machining line of a major automobile manufacturer based in western India. Company policy requires that raw material be kept in stock at least one day in advance, so an order placed on a given day is delivered and ready for use only from the next day onward, unless a delay is stated.
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Units | 50 | 25 | 30 | 20 | 5 | 6 | 2 | 10 | 15 | 20 | 25 | 10 | 5 | 20 | 10 |
Question: 1
If the raw material inventory on Day 0 was 165 units, the manager needs to place an order latest by which day?
If the raw material inventory on Day 0 was 165 units, the manager needs to place an order latest by which day?
Show Hint
Track the day-0 stock minus the running total of daily requirements, and remember an order placed on a day only becomes usable from the next day.
Updated On: Jul 13, 2026
- 8th
- 9th
- 10th
- 11th
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Understand the rule.
The company keeps raw material at least one day ahead. This means an order placed on any day arrives and is ready for use only from the next day onward. So the manager must place the order before the stock runs short, not on the same day it runs short.
Step 2: Track the running stock day by day.
Start with 165 units on Day 0. Subtract each day's requirement from the table to get the stock left at the end of that day.
End of Day 1: \(165 - 50 = 115\)
End of Day 2: \(115 - 25 = 90\)
End of Day 3: \(90 - 30 = 60\)
End of Day 4: \(60 - 20 = 40\)
End of Day 5: \(40 - 5 = 35\)
End of Day 6: \(35 - 6 = 29\)
End of Day 7: \(29 - 2 = 27\)
End of Day 8: \(27 - 10 = 17\)
End of Day 9: \(17 - 15 = 2\)
Step 3: Find the day the stock falls short.
Day 10 needs 20 units, but only 2 units are left at the start of Day 10 (carried over from the end of Day 9). That is a shortfall, so fresh material must be in hand before Day 10 begins.
Step 4: Work out the latest order day.
Since an order placed on a day is ready only from the next day, the order must go in on Day 9 so it is ready in time for Day 10's requirement. Placing it any later, say on Day 10 itself, would mean Day 10's production is already short.
Final Answer:
The manager must place the order latest by the 9th day.
\[ \boxed{9^{th} \text{ day}} \]
The company keeps raw material at least one day ahead. This means an order placed on any day arrives and is ready for use only from the next day onward. So the manager must place the order before the stock runs short, not on the same day it runs short.
Step 2: Track the running stock day by day.
Start with 165 units on Day 0. Subtract each day's requirement from the table to get the stock left at the end of that day.
End of Day 1: \(165 - 50 = 115\)
End of Day 2: \(115 - 25 = 90\)
End of Day 3: \(90 - 30 = 60\)
End of Day 4: \(60 - 20 = 40\)
End of Day 5: \(40 - 5 = 35\)
End of Day 6: \(35 - 6 = 29\)
End of Day 7: \(29 - 2 = 27\)
End of Day 8: \(27 - 10 = 17\)
End of Day 9: \(17 - 15 = 2\)
Step 3: Find the day the stock falls short.
Day 10 needs 20 units, but only 2 units are left at the start of Day 10 (carried over from the end of Day 9). That is a shortfall, so fresh material must be in hand before Day 10 begins.
Step 4: Work out the latest order day.
Since an order placed on a day is ready only from the next day, the order must go in on Day 9 so it is ready in time for Day 10's requirement. Placing it any later, say on Day 10 itself, would mean Day 10's production is already short.
Final Answer:
The manager must place the order latest by the 9th day.
\[ \boxed{9^{th} \text{ day}} \]
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Question: 2
If the raw material inventory on Day 0 was 73 units and the manager orders 17, 53 and 86 units on the first, second and fourth day respectively, when does he need to order next?
If the raw material inventory on Day 0 was 73 units and the manager orders 17, 53 and 86 units on the first, second and fourth day respectively, when does he need to order next?
Show Hint
Add each order to stock only from the day after it is placed, then find the first day the running balance cannot cover the requirement.
Updated On: Jul 13, 2026
- 10th day
- 11th day
- 13th day
- 14th day
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Note when each order becomes usable.
The one-day-advance rule means an order placed on Day 1 is ready from Day 2, an order placed on Day 2 is ready from Day 3, and an order placed on Day 4 is ready from Day 5.
Step 2: Build the day-wise stock, adding orders when they arrive.
Opening stock is 73 units.
Day 1: start with 73, no order arrives yet, use 50. End of Day 1: \(73 - 50 = 23\)
Day 2: 17 units (ordered Day 1) arrive, start \(23 + 17 = 40\), use 25. End of Day 2: \(40 - 25 = 15\)
Day 3: 53 units (ordered Day 2) arrive, start \(15 + 53 = 68\), use 30. End of Day 3: \(68 - 30 = 38\)
Day 4: no arrival yet, use 20. End of Day 4: \(38 - 20 = 18\)
Day 5: 86 units (ordered Day 4) arrive, start \(18 + 86 = 104\), use 5. End of Day 5: \(104 - 5 = 99\)
Step 3: Continue with no more orders and watch the stock fall.
Day 6: \(99 - 6 = 93\)
Day 7: \(93 - 2 = 91\)
Day 8: \(91 - 10 = 81\)
Day 9: \(81 - 15 = 66\)
Day 10: \(66 - 20 = 46\)
Day 11: \(46 - 25 = 21\)
Day 12: \(21 - 10 = 11\)
Day 13: \(11 - 5 = 6\)
Step 4: Find where the stock runs short.
Day 14 needs 20 units, but only 6 units remain at the start of Day 14. That is a shortfall, so material must arrive in time for Day 14.
Step 5: Apply the one day advance rule.
An order placed on Day 13 is ready from Day 14, exactly when it is needed. So the manager must place the next order on Day 13.
Final Answer:
The manager needs to order next on the 13th day.
\[ \boxed{13^{th} \text{ day}} \]
The one-day-advance rule means an order placed on Day 1 is ready from Day 2, an order placed on Day 2 is ready from Day 3, and an order placed on Day 4 is ready from Day 5.
Step 2: Build the day-wise stock, adding orders when they arrive.
Opening stock is 73 units.
Day 1: start with 73, no order arrives yet, use 50. End of Day 1: \(73 - 50 = 23\)
Day 2: 17 units (ordered Day 1) arrive, start \(23 + 17 = 40\), use 25. End of Day 2: \(40 - 25 = 15\)
Day 3: 53 units (ordered Day 2) arrive, start \(15 + 53 = 68\), use 30. End of Day 3: \(68 - 30 = 38\)
Day 4: no arrival yet, use 20. End of Day 4: \(38 - 20 = 18\)
Day 5: 86 units (ordered Day 4) arrive, start \(18 + 86 = 104\), use 5. End of Day 5: \(104 - 5 = 99\)
Step 3: Continue with no more orders and watch the stock fall.
Day 6: \(99 - 6 = 93\)
Day 7: \(93 - 2 = 91\)
Day 8: \(91 - 10 = 81\)
Day 9: \(81 - 15 = 66\)
Day 10: \(66 - 20 = 46\)
Day 11: \(46 - 25 = 21\)
Day 12: \(21 - 10 = 11\)
Day 13: \(11 - 5 = 6\)
Step 4: Find where the stock runs short.
Day 14 needs 20 units, but only 6 units remain at the start of Day 14. That is a shortfall, so material must arrive in time for Day 14.
Step 5: Apply the one day advance rule.
An order placed on Day 13 is ready from Day 14, exactly when it is needed. So the manager must place the next order on Day 13.
Final Answer:
The manager needs to order next on the 13th day.
\[ \boxed{13^{th} \text{ day}} \]
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Question: 3
If the raw material supplier starts acting unreliable and delays deliveries by 48 hours, which day's production will be hit if the starting inventory on Day 0 is 163 units and an order is placed on the morning of Day 7?
If the raw material supplier starts acting unreliable and delays deliveries by 48 hours, which day's production will be hit if the starting inventory on Day 0 is 163 units and an order is placed on the morning of Day 7?
Show Hint
First find the day the stock would run out with no order at all, then compare the delayed arrival day against that day.
Updated On: Jul 13, 2026
- None
- Day 8
- Day 9
- Day 10
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Track the stock without any order, starting from 163 units.
End of Day 1: \(163 - 50 = 113\)
End of Day 2: \(113 - 25 = 88\)
End of Day 3: \(88 - 30 = 58\)
End of Day 4: \(58 - 20 = 38\)
End of Day 5: \(38 - 5 = 33\)
End of Day 6: \(33 - 6 = 27\)
End of Day 7: \(27 - 2 = 25\)
End of Day 8: \(25 - 10 = 15\)
End of Day 9: \(15 - 15 = 0\)
Step 2: Check whether Day 8 and Day 9 need the new order.
Day 8 needs 10 units and 25 are on hand, so it is safe. Day 9 needs 15 units and exactly 15 are on hand, so the requirement is used up exactly, with nothing missing. Neither day is hit.
Step 3: Work out when the Day 7 order was due to arrive.
The order is placed on the morning of Day 7. Under the normal one-day-advance rule, it would arrive on Day 8. Since fresh material is not actually needed until Day 10 (the stock lasts exactly through Day 9), placing the order on Day 7 already builds in extra safety margin.
Step 4: Apply the 48 hour delay.
A 48 hour delay pushes the delivery back by 2 more days, from Day 8 to Day 10. Day 10 is precisely the day fresh material is first required, since the stock runs out exactly at the end of Day 9. So the delayed order still lands just in time, on the morning of Day 10, before that day's production begins.
Step 5: Conclude which day's production is hit.
Because the order still arrives in time for the first day it is actually needed, no day's production is disrupted by the delay.
Final Answer:
No day's production is hit, so the answer is None.
\[ \boxed{\text{None}} \]
End of Day 1: \(163 - 50 = 113\)
End of Day 2: \(113 - 25 = 88\)
End of Day 3: \(88 - 30 = 58\)
End of Day 4: \(58 - 20 = 38\)
End of Day 5: \(38 - 5 = 33\)
End of Day 6: \(33 - 6 = 27\)
End of Day 7: \(27 - 2 = 25\)
End of Day 8: \(25 - 10 = 15\)
End of Day 9: \(15 - 15 = 0\)
Step 2: Check whether Day 8 and Day 9 need the new order.
Day 8 needs 10 units and 25 are on hand, so it is safe. Day 9 needs 15 units and exactly 15 are on hand, so the requirement is used up exactly, with nothing missing. Neither day is hit.
Step 3: Work out when the Day 7 order was due to arrive.
The order is placed on the morning of Day 7. Under the normal one-day-advance rule, it would arrive on Day 8. Since fresh material is not actually needed until Day 10 (the stock lasts exactly through Day 9), placing the order on Day 7 already builds in extra safety margin.
Step 4: Apply the 48 hour delay.
A 48 hour delay pushes the delivery back by 2 more days, from Day 8 to Day 10. Day 10 is precisely the day fresh material is first required, since the stock runs out exactly at the end of Day 9. So the delayed order still lands just in time, on the morning of Day 10, before that day's production begins.
Step 5: Conclude which day's production is hit.
Because the order still arrives in time for the first day it is actually needed, no day's production is disrupted by the delay.
Final Answer:
No day's production is hit, so the answer is None.
\[ \boxed{\text{None}} \]
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Question: 4
Suppose the raw material inventory on Day 0 was 73 units and the manager orders 17, 53 and 86 units on the first, second and fourth day respectively, so that the next order falls due on Day 13. If the cost of placing an order is Rs. 650 per order, find the minimum cost incurred over the whole 15 day cycle.
Suppose the raw material inventory on Day 0 was 73 units and the manager orders 17, 53 and 86 units on the first, second and fourth day respectively, so that the next order falls due on Day 13. If the cost of placing an order is Rs. 650 per order, find the minimum cost incurred over the whole 15 day cycle.
Show Hint
Count the fewest orders that keep stock non negative through all 15 days, then multiply by Rs. 650 per order.
Updated On: Jul 13, 2026
- Rs. 1,950
- Rs. 650
- Rs. 2,600
- Rs. 3,250
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Recall the order pattern from the earlier scenario.
Opening stock is 73 units. Orders are placed on Day 1 (17 units), Day 2 (53 units) and Day 4 (86 units). Working through the day-wise stock shows the next order is due on Day 13, and the stock at the start of Day 14 is 6 units.
Step 2: Find the minimum order size that finishes the cycle.
From Day 14 onward, the total requirement is \(20 + 10 = 30\) units (Day 14 needs 20, Day 15 needs 10). With 6 units already on hand, the Day 13 order needs to bring in only \(30 - 6 = 24\) units to exactly finish the 15 day cycle with nothing left over.
Step 3: Check that no further order is needed.
Since a single order of 24 units placed on Day 13 covers both Day 14 and Day 15 completely, there is no need for a fifth order. This keeps the number of orders at the minimum possible.
Step 4: Count the total number of orders over the 15 day cycle.
The orders fall on Day 1, Day 2, Day 4 and Day 13, that is 4 orders in total.
Step 5: Work out the minimum total cost.
Each order costs Rs. 650, no matter how many units are in it.
\[ 4 \times 650 = 2600 \]
Final Answer:
The minimum cost incurred over the whole 15 day cycle is Rs. 2,600.
\[ \boxed{Rs.\ 2600} \]
Opening stock is 73 units. Orders are placed on Day 1 (17 units), Day 2 (53 units) and Day 4 (86 units). Working through the day-wise stock shows the next order is due on Day 13, and the stock at the start of Day 14 is 6 units.
Step 2: Find the minimum order size that finishes the cycle.
From Day 14 onward, the total requirement is \(20 + 10 = 30\) units (Day 14 needs 20, Day 15 needs 10). With 6 units already on hand, the Day 13 order needs to bring in only \(30 - 6 = 24\) units to exactly finish the 15 day cycle with nothing left over.
Step 3: Check that no further order is needed.
Since a single order of 24 units placed on Day 13 covers both Day 14 and Day 15 completely, there is no need for a fifth order. This keeps the number of orders at the minimum possible.
Step 4: Count the total number of orders over the 15 day cycle.
The orders fall on Day 1, Day 2, Day 4 and Day 13, that is 4 orders in total.
Step 5: Work out the minimum total cost.
Each order costs Rs. 650, no matter how many units are in it.
\[ 4 \times 650 = 2600 \]
Final Answer:
The minimum cost incurred over the whole 15 day cycle is Rs. 2,600.
\[ \boxed{Rs.\ 2600} \]
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Question: 5
If the daily pilferage is 5 units, find the minimum number of units that need to be ordered through the whole cycle, given that the inventory on Day 0 is 100 units and the inventory ends at zero after Day 15.
If the daily pilferage is 5 units, find the minimum number of units that need to be ordered through the whole cycle, given that the inventory on Day 0 is 100 units and the inventory ends at zero after Day 15.
Show Hint
Total units leaving stock equal the sum of daily requirements plus daily pilferage; total ordered equals that sum minus the opening stock.
Updated On: Jul 13, 2026
- 296
- 153
- 75
- 228
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Add up the total production requirement for all 15 days.
Sum the Units row of the table:
\[ 50+25+30+20+5+6+2+10+15+20+25+10+5+20+10 = 253 \]
Step 2: Add the pilferage lost over the same period.
Pilferage removes 5 units every day, for 15 days:
\[ 5 \times 15 = 75 \]
Step 3: Find the total units that leave the stock.
Total units leaving stock equal the production requirement plus the pilferage:
\[ 253 + 75 = 328 \]
Step 4: Subtract the opening stock, since the cycle must end at zero.
The plant starts with 100 units on Day 0 and must end with 0 units after Day 15. So the units that must be brought in through orders make up the rest:
\[ 328 - 100 = 228 \]
Step 5: Confirm this is the minimum.
This total of 228 units is the least that can be ordered, since ordering any less would leave the stock short of covering both production and pilferage somewhere in the 15 days, while ordering more would leave a positive balance at the end, which contradicts ending at zero.
Final Answer:
The minimum number of units to be ordered through the whole cycle is 228.
\[ \boxed{228} \]
Sum the Units row of the table:
\[ 50+25+30+20+5+6+2+10+15+20+25+10+5+20+10 = 253 \]
Step 2: Add the pilferage lost over the same period.
Pilferage removes 5 units every day, for 15 days:
\[ 5 \times 15 = 75 \]
Step 3: Find the total units that leave the stock.
Total units leaving stock equal the production requirement plus the pilferage:
\[ 253 + 75 = 328 \]
Step 4: Subtract the opening stock, since the cycle must end at zero.
The plant starts with 100 units on Day 0 and must end with 0 units after Day 15. So the units that must be brought in through orders make up the rest:
\[ 328 - 100 = 228 \]
Step 5: Confirm this is the minimum.
This total of 228 units is the least that can be ordered, since ordering any less would leave the stock short of covering both production and pilferage somewhere in the 15 days, while ordering more would leave a positive balance at the end, which contradicts ending at zero.
Final Answer:
The minimum number of units to be ordered through the whole cycle is 228.
\[ \boxed{228} \]
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