The Way Time Grocery chain operates in major areas North-western part of Mindanao. The stores have a "no-frills" approach, with low overhead and high volume. They generally buy their stock in volume at low prices. However, in some cases they actually buy stock at stores in other areas and ship it in. They can made this because of high prices in the cities they operate in compared with costs in other locations. One example is baby food. Way Time purchases baby food at stores in Zamboanga, Bacolod, Cebu, Dumaguete, and Ozamis and then ships it to six stores in and around Dipolog. The stores in the outlying areas know what Way Time is up to, so they limit the number of cases of baby food Way Time can purchase. The following table shows the profit Way Time makes per case of baby food, based on where the chain purchases it and at which store it is sold, plus the available baby food per week at purchase locations and the shelf space available at each Way Time store per week:

Way Time Store (profit/case) in thousand pesos

Purchase Location 1 2 3 4 5 6 Supply

Zamboanga 9 8 11 12 7 8 26

Bacolod 10 10 8 6 9 7 40

Cebu 8 6 6 5 7 4 20

Dumaguete 4 6 9 5 8 10 40

Ozamis 12 10 8 9 6 7 45

Demand 25 15 30 18 27 35

Determine where Easy Time should purchase baby food and how the food should be distributed to maximize profit.

3.1 Suppose that in Problem 3 Way Time can purchase all the baby food it needs from a Dipolog City distributor at a price that will result in a profit of 9,000 per case at stores 1, 3, and 4; 8,000 per case at stores 2 and 6; and 7,000 per case at store 5. Should Way Time purchase all, none, or some of its baby food from the distributor rather than purchase it at other stores and truck it in?