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 all the units should be sent to the market, then on which days should the trucks be hired to minimize the cost?

• A. 2nd, 4th, 6th, 7th
• B. 7th
• C. 2nd, 4th, 5th, 7th
• D. None of these

Hint:

When minimizing cost, always consider both the storage cost and the truck's capacity. Hire the truck on the days where production exceeds the capacity.

Answer 1

The Correct Option is A

We are given that the truck can carry 2,000 cubic feet per day, and the hiring cost per day is Rs. 1,000. The storing cost is Rs. 5 per cubic foot per day. We want to minimize the cost by determining the best days to hire the truck.
Step 1: Calculate the excess production each day We need to calculate the excess production that cannot be stored and must be sent to the market immediately. For each day, we subtract the truck's capacity (2,000 cubic feet) from the units produced:
- Day 1: 150 units (no excess, all can be stored)
- Day 2: 180 units (no excess, all can be stored)
- Day 3: 120 units (no excess, all can be stored)
- Day 4: 250 units (no excess, all can be stored)
- Day 5: 160 units (no excess, all can be stored)
- Day 6: 120 units (no excess, all can be stored)
- Day 7: 150 units (no excess, all can be stored)
Thus, to minimize costs, we should hire the truck only on days where the excess units cannot be stored and must be sent to the market.
Step 2: Minimize costs
The minimum cost occurs when the truck is hired only on the days when the total units exceed the truck’s capacity. After analyzing the production and storage, it is evident that hiring the truck on days 2, 4, 5, and 7 will minimize the cost.
The correct answer is Option 3: 2nd, 4th, 5th, 7th.