Question 1

Paul Restaurant is a company producing and delivering nutritious dog food to retail stores and dog daycares. Due to the recent spike in dog adoption, the demand for dog food has substantially increased. Paul Restaurant has more clients requesting dog food delivery than last year.

Billy Wilson is a manager at Paul Restaurant. He would like to explore ways to reduce delivery distances since the company needs to visit multiple delivery locations.

Table 1. Distance between DC and each customer

Distance (km)	Store 1	Store 2	Store 3	Daycare 1	Daycare 2	DC
Store 1	-	33	2	4	28	9
Store 2		-	25	48	12	29
Store 3			-	19	18	26
Daycare 1				-	40	44
Daycare 2					-	25

Billy Wilson began by calculating distances when the company uses a small van which can only deliver dog food to one place per tour due to the loading capacity. In other words, the small van must return to the DC after completing a delivery job.

Question 1.1: Use information on Table 1. What is the total distance (in km) that the van needs to travel to serve all stores and dog daycares?

Round your answer to the nearest integer.

Question 2

To improve the delivery system, Billy Wilson would like to examine if hiring a large truck that can carry dog food for all clients at once could reduce the distance. In other words, there is no loading capacity constraint for the truck.

Question 2.1:Apply the nearest neighbor technique on Table 1 data and calculate the shortest distance (in km) starting from DC, visiting all clients, and returning to DC.

Round your answer to the nearest integer.

Question 3

Now, Billy Wilson would like to see if applying the Clark-Wright savings algorithm can save more distance. He is still hiring the same large truck which can carry all the dog food needed. Therefore there is no loading capacity constraint for the truck.

What is the greatest savings (in km) Billy Wilson can get from pairing from two clients in one tour? Use information on Table 1.

Round your answer to the nearest integer.

Question 4

Unfortunately, the truck company is out of the large truck Billy Wilson used to hire due to a big festival in the town nearby. Furthermore, a small van he used before needs repairs. Instead, Billy can hire a van with a capacity of 150 units.

Table 2. Dog food demand (units) per each customer

Customer	Store 1	Store 2	Store 3	Daycare 1	Daycare 2
Demand (units)	66	114	70	55	67

Using the demand of each customer presented on Table 2 above, calculate how many routes the van needs to make to complete delivery.

Round your answer to the nearest integer.