Johnson Dairy procures milk from several areas, mainly from milk producers in villages, processes milk at their facilities and sells milk in packets in different cities with different prices.

Since differential pricing is adopted, the profit per liter of milk also varies from place to place.

The following table shows the profit per liter of milk in rupees if procured from a specific village and sold in a specific city.

From To City (profit per liter, in E)
C1 C2 C3 C4 C5 Supply in liters Village 1 9 8 11 12 7 1000 Village 2 10 10 8 6 9 1400 Village 3 8 6 6 5 7 2100 Village 4 4 6 9 5 8 1250 Village 5 12 10 8 9 6 1450 Demand in liters 1150 1450 1600 1800 1400 Families in City 1 buy milk in 250-ml packs and families in City 2 buy milk in 500-ml packs;
whereas families in Cities 3, 4, and 5 buy milk in 1-liter packs. The company wants to maximize its profit.

a. Determine the number of packs of milk distributed across cities that maximizes the profit.

b. Will the solution change if the company decides to pack all the procured milk in 250-ml packs?

c. If the company decides to supply City 3 from only Village 3 for logistics reasons, what is the effect on the profit?