Precise buoy placement is crucial for the system to work efficiently. If two buoys are placed too close together, the signals they transmit may overlap, interrupting the signal’s transmission.

They need to determine the optimal placement of three relay buoys along a 6.4 Nautical miles path to maximize the signal strength at the receiver. The students are given these conditions: Signal overlap occurs if two buoys are within 1.5 Nautical miles of each other.

Nine relay buoys, labeled A to I, boost the signal strength by covering the distance between the receiving station and the submarines. For various reasons, the buoys move in the direction of the submarine at various speeds/paces. The placement of the buoys is done at 1.30 pm on the day the research starts, after 15 minutes the team found some weak signals received from the submarines to the receiving station which represents the overlap in some buoys.

Question:

Given the1.5 Nautical miles overlap condition, can you help the students figure out which buoys will overlap on the path after the 15th minute?

The pace and distance of the buoys are mentioned in the reference image.

However, the buoys' efficiency is sensitive to changes in surface temperature. For every 10°F increase in surface temperature, the efficiency of the buoys decreases by 5%.

Due to a rise in surface temperature, the buoys are not operating at their full capacity. The first buoy received 100 units but transmitted only 190 units of the expected signal instead of 200. The second buoy, which should have amplified the 190 units to 380 units, transmitted only 342 units. Similarly, the third buoy transmitted 615.6 units to the research center instead of the expected 684 units.

These observations indicate that the efficiency of the first, second, and third buoys has decreased, affecting the overall signal strength reaching the research center.

Question:

Under the new conditions, the following observations were made:

Buoy A received 100, and transmitted 190 units to Buoy B.

Buoy B received 190, and transmitted 342 Units to Buoy C.

Buoy C received 342, and transmitted 615.6 units to the receiving station.

Given this information, what is the temperature increase (from the optimal condition) in each buoy’s zone?

Refer Referance Image for the formula.

FreshGro also wants to explore how traffic conditions impact delivery efficiency.

The dataset includes the following fields.

Refer table from the Referance Image.

FreshGro provides the following sample dataset.

Refer table from the Referance Image.

Question:

1. How do traffic conditions (Low, Moderate, High) impact the efficiency scores for City A?

2. Based on the overall analysis, which city is the most efficient?

The platform’s delivery vehicle operates under the following constraints:

Average Speed (no load): 50 km/h.

Weight Impact: For every additional kilogram of the order, the speed decreases by 1%.

Distance Impact: Delivery times are calculated using the adjusted speed.

A route consists of deliveries to the following customers:

Customer A: 15 km away, order weight 10 kg.

Customer B: 20 km further from Customer A, order weight 15 kg.

Customer C: 10 km further from Customer B, order weight 5 kg.

Question: What is the total time taken to complete the deliveries to all customers?