An oil company produces three brands of oils: Regular, Multi grade, and Supreme. Each brand of oil is composed of one or more of four crude stocks, each having a different viscosity index. The relevant data concerning the crude stocks are:

Each brand of oil must meet a minimum standard for viscosity index, and each brand thus sells at a different price. The relevant data concerning the three brands of oil are:

Determine an optimal production plan for a single day, assuming that all oil produced during this day can be either sold or stored at negligible cost. This exercise is subject to alternative interpretations. Use a model to investigate the following distinct situations:
a. The daily demands represent potential sales. In other words, the model should contain demand ceilings (upper limits). What is the optimal profit under these assumptions?
b. The daily demands are to be met precisely. In other words, the model should contain demand constraints in the form of equalities. What is the optimal profit under these assumptions?
c. The daily demands represent minimum sales commitments, but all output can be sold. In other words, the model should permit production to exceed daily demand. What is the optimal profit under these assumptions?

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Supply Per Day (barrels) Crude Viscosity Cost ($/barrel) Stock Index 1,000 20 40 30 55 7.10 8.50 2 1,100 1,200 1,100 7.70 4 9.00 4. Selling Price ($/barrel) Daily Demand (barrels) Minimum Brand Viscosity Index 25 35 50 8.50 Regular Multigrade 2,000 1,500 Supreme 9.00 10.00 750