i) To determine which store should be called for a pizza delivery to the point (6, 2), we need to calculate the distance from each store to the delivery point and choose the store with the shortest distance.
Using the distance formula, d = √[(x2 - x1)^2 + (y2 - y1)^2], we can calculate the distances as follows:
Distance from store (2, 2) to (6, 2):
d1 = √[(6 - 2)^2 + (2 - 2)^2]
d1 = √[4^2 + 0^2]
d1 = √16
d1 = 4 units
Distance from store (9, -2) to (6, 2):
d2 = √[(6 - 9)^2 + (2 - (-2))^2]
d2 = √[(-3)^2 + 4^2]
d2 = √9 + 16
d2 = √25
d2 = 5 units
Distance from store (9, 5) to (6, 2):
d3 = √[(6 - 9)^2 + (2 - 5)^2]
d3 = √[(-3)^2 + (-3)^2]
d3 = √9 + 9
d3 = √18
d3 ≈ 4.24 units
Comparing the distances, we find that the shortest distance is from store (2, 2) to the delivery point (6, 2), which is 4 units. Therefore, store (2, 2) should be called for the pizza delivery.
ii) The answer for part i may not always be the best for a pizza company in different circumstances. Here are a few factors that could change the optimal store choice:
- **Traffic conditions:** If there is heavy traffic or congestion on the roads, the delivery time may be affected, and a store that is farther away but has a clearer route may be a better choice.
- **Delivery capacity:** If one store is experiencing a high volume of orders or has limited delivery drivers, it may not be able to meet the 30-minute guarantee, even if it is the closest store. In such cases, another store with more available resources may be a better option.
- **Customer preferences:** Some customers may have specific preferences for a particular store based
