Question:
Production pattern for number of units (in cubic feet) per day
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 the storage cost is reduced to Re 0.80 per cubic feet per day, then on which day(s), should the truck be hired?
Production pattern for number of units (in cubic feet) per day
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 the storage cost is reduced to Re 0.80 per cubic feet per day, then on which day(s), should the truck be hired?
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When storage costs are reduced, hiring the truck on the days with excess production becomes less expensive. Always compare the storage cost with the truck's hiring cost to find the optimal days.
Updated On: Aug 4, 2025
- 4th
- 7th
- 4th and 7th
- None of these
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The Correct Option is B
Solution and Explanation
Now, the storage cost is Rs. 0.80 per cubic foot per day. We calculate the excess units produced and determine the optimal day(s) to hire the truck, considering the new storage cost.
Step 1: Calculate excess production
Again, for each day, we calculate the excess units: - Day 1: 150 units (can be stored)
- Day 2: 180 units (can be stored)
- Day 3: 120 units (can be stored)
- Day 4: 250 units (can be stored)
- Day 5: 160 units (can be stored)
- Day 6: 120 units (can be stored)
- Day 7: 150 units (can be stored)
Step 2: Minimize costs
Now that the storage cost is reduced to Rs. 0.80 per cubic foot, we need to calculate which days offer the minimum cost when the truck should be hired. Upon analysis, hiring the truck on the 7th day would be optimal for minimizing costs, as the storage costs would not outweigh the truck's hiring cost.
Thus, the correct answer is Option 2: 7th.
Step 1: Calculate excess production
Again, for each day, we calculate the excess units: - Day 1: 150 units (can be stored)
- Day 2: 180 units (can be stored)
- Day 3: 120 units (can be stored)
- Day 4: 250 units (can be stored)
- Day 5: 160 units (can be stored)
- Day 6: 120 units (can be stored)
- Day 7: 150 units (can be stored)
Step 2: Minimize costs
Now that the storage cost is reduced to Rs. 0.80 per cubic foot, we need to calculate which days offer the minimum cost when the truck should be hired. Upon analysis, hiring the truck on the 7th day would be optimal for minimizing costs, as the storage costs would not outweigh the truck's hiring cost.
Thus, the correct answer is Option 2: 7th.
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