2.5 Oil Blending: An oil company produces three brands of oil: regular, multigrade, and supreme. Each brand of oil is composed of one or more of four crude stocks, each having a different lubrication index. The relevant data concerning the crude stocks are as follows. Crude Stock Lubrication Index Cost ($/Barrel) Daily Supply (Barrels) 1 2 3 4 20 40 30 55 7.1 8.5 7.7 .9 1000 1100 1200 1100 Each brand of oil must meet a minimum standard for a lubrication index, and each brand thus sells at a different price. The relevant data concerning the three brands of oil are as follows. Brand Regular Minimum Lubrication Index 25 Multigrade 35 Supreme 50 Selling Price ($/Barrel) 8.5 9 10 Daily Demand (Barrels) 2000 1500 .750 The task is to determine an optimal output plan for a single day, assuming that production can be either sold or else stored at negligible cost. The daily demand figures are subject to alternative interpretations. Investigate the following. a. The daily demands represent potential sales. In other words, the model should contain demand ceilings (upper limits). What is the optimal profit? b. The daily demands are strict obligations. In other words, the model should contain demand constraints that are met precisely. What is the optimal profit? c. The daily demands represent minimum sales commitments, but all output can be sold. In other words, the model should permit production to exceed the daily commitments. What is the optimal profit?