Q1 LOGICAL PUZZLES
For a truck that can carry 2,000 cubic ft, hiring cost per day is Rs. 1,000. Storing cost per cubic feet is Rs. 5 per day. If all the units should be sent to the market, then on which days should the trucks be hired to minimize the cost?
|
Day |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
Number of units |
150 |
180 |
120 |
250 |
160 |
120 |
150 |
To minimize the cost, we need to
calculate the total cost of hiring and storing for each day and choose the days
with the minimum cost.
Total cost for each day can be calculated as follows:
- Day 1: Hiring cost = Rs. 1000, Storing cost = Rs. 5 * 150 = Rs. 750, Total cost = Rs. 1750
- Day 2: Hiring cost = Rs. 1000, Storing cost = Rs. 5 * (150 + 180) = Rs. 1650, Total cost = Rs. 2650
- Day 3: Hiring cost = Rs. 0 (no units produced), Storing cost = Rs. 5 * (150 + 180 + 120) = Rs. 2250, Total cost = Rs. 2250
- Day 4: Hiring cost = Rs. 1000, Storing cost = Rs. 5 * (150 + 180 + 120 + 250) = Rs. 3250, Total cost = Rs. 4250
- Day 5: Hiring cost = Rs. 0 (no units produced), Storing cost = Rs. 5 * (150 + 180 + 120 + 250 + 160) = Rs. 4000, Total cost = Rs. 4000
- Day 6: Hiring cost = Rs. 0 (no units produced), Storing cost = Rs. 5 * (150 + 180 + 120 + 250 + 160 + 120) = Rs. 5200, Total cost = Rs. 5200
- Day 7: Hiring cost = Rs. 1000, Storing cost = Rs. 5 * (150 + 180 + 120 + 250 + 160 + 120 + 150) = Rs. 5750, Total cost = Rs. 6750
Therefore, the days with minimum cost are 2nd, 4th, 5th, and 7th.
Hence, the answer is (c) 2nd, 4th, 5th, 7th
Total cost for each day can be calculated as follows:
- Day 1: Hiring cost = Rs. 1000, Storing cost = Rs. 5 * 150 = Rs. 750, Total cost = Rs. 1750
- Day 2: Hiring cost = Rs. 1000, Storing cost = Rs. 5 * (150 + 180) = Rs. 1650, Total cost = Rs. 2650
- Day 3: Hiring cost = Rs. 0 (no units produced), Storing cost = Rs. 5 * (150 + 180 + 120) = Rs. 2250, Total cost = Rs. 2250
- Day 4: Hiring cost = Rs. 1000, Storing cost = Rs. 5 * (150 + 180 + 120 + 250) = Rs. 3250, Total cost = Rs. 4250
- Day 5: Hiring cost = Rs. 0 (no units produced), Storing cost = Rs. 5 * (150 + 180 + 120 + 250 + 160) = Rs. 4000, Total cost = Rs. 4000
- Day 6: Hiring cost = Rs. 0 (no units produced), Storing cost = Rs. 5 * (150 + 180 + 120 + 250 + 160 + 120) = Rs. 5200, Total cost = Rs. 5200
- Day 7: Hiring cost = Rs. 1000, Storing cost = Rs. 5 * (150 + 180 + 120 + 250 + 160 + 120 + 150) = Rs. 5750, Total cost = Rs. 6750
Therefore, the days with minimum cost are 2nd, 4th, 5th, and 7th.
Hence, the answer is (c) 2nd, 4th, 5th, 7th
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