2) Valvolime 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 (S/Barrel) Daily Supply [Barrels] 1 20 7.1 1000 2 40 3.5 1100 3 30 7.7 1200 4 55 9 1100 Each brand of oil must meet a 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 Minimum Lubrication Cost (S/Barrel) Daily Demand (Barrels) Index Regular 25 3.5 2000 Multigrade 35 9 1500 Supreme 50 10 750 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 gures 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 the production to exceed the daily commitments. What is the optimal profit? Your submission to this question should be a spreadsheet containing a Solver Model for each part. Please make sure to answer the questions explicitly in words. Your Solver Model needs to be clear so that someone who looks at it can follow what you are doing without going into Solver (use colors 'for decision variables, objective, constraints etc as in the examples). If necessary, explain the equations you are modeling mathematically. Make sure to also paste your Solver dialog box in the spreadsheet. Explain how you change the models between parts a, b, and c