GATE Technical: ME questions with solutions

Q1. Annual demand for window frames is 10000. Each frame costs Rs. 200 and ordering cost is Rs. 300 per order. Inventory holding cost is Rs. 40 per frame per year. The supplier is willing to offer 2% discount if the order quantity is 1000 or more, and 4% if order quantity is 2000 or more. If the total cost is to be minimized, the retailer should

1. order 200 frames every time
2. accept 2% discount
3. accept 4% discount
4. order Economic Order Quantity

Answer: accept 4% discount

Accepting the 4% discount is the best option because it reduces the overall cost per frame significantly when ordering in larger quantities, which aligns with the goal of minimizing total costs. This discount, combined with the optimal order quantity, leads to lower purchasing and holding costs.

Q2. The project activities, precedence relationships and durations are described in the table. The critical path of the project is Activity | Precedence | Duration (in days) P | - | 3 Q | - | 4 R | P | 5 S | Q | 5 T | R, S | 7 U | R, S | 5 V | T | 2 W | U | 10

1. P-R-T-V
2. Q-S-T-V
3. P-R-U-W
4. Q-S-U-W

Answer: Q-S-U-W

The critical path is the longest sequence of activities that determines the shortest time to complete the project. In this case, the path Q-S-U-W has the longest total duration of 24 days, making it the critical path.