Minimum Flow Problem

An oil field can produce 10,000 barrels of crude oil a week. For the next four weeks, you are contracted to deliver 1,000, 5,000, 7,000 and 20,000 barrels of crude oil to a refinery. Suppose that the cost to extract oil is $5, $1, $1, $4 per barrel in each week respectively. You can also store oil at cost of $3 per barrel per week. i. Draw a network, so that solving a min-cost-max-flow problem on it delivers the optimal oil production plan. ii. Now, suppose that you only have capacity to store $3,000 barrels on site. You can store more at an external location at cost of $10 per barrel. Update your network to allow for this option