$(1)$ Oilco has oil fields in San Diego and Los Angeles. The San Diego field can produce $500,000$ barrels

per day, and the Los Angeles field can produce $400,000$ barrels per day. Oil is sent from the fields to a

refinery, either in Dallas or in Houston $($assuming that each refinery has unlimited capacity$).$ It costs

$$700$ to refine $100,000$ barrels of oil at Dallas and $$900$ at Houston. Refined oil is shipped to customers

in Chicago and New York. Chicago customers require $400,000$ barrels per day of refined oil; New York

customers require $300,000.$ The costs of shipping $100,000$ barrels of oil $($refined or unrefined$)$ between

cities are given in Table. Give a balanced transportation tableau for this situation.