Problem 3: Floataway Tours has $400,000 that may be used to purchase new rental boats for hire during the summer. The boats can be purchased from two different manufacturers. Pertinent data concerning the boats are summarized here: Boat Manufacturer Cost Maximum Seating 3 Speedhawk Silverbird Catman Classy 5 Sleekbot Sleekbot Racer Racer Expected Daily Profit $70 $80 $50 $110 $6,000 $7,000 $5,000 $9,000 2 6 Floataway Tours would like to purchase at least 50 boats, and would like to purchase the same number from Sleekboat as from Racer to maintain goodwill. In addition, Floataway Tours wishes to have a total seating capacity of at least 200. Formulate this problem as a linear program. You need not solve. Problem 4: A heating-oil distributor blends two grades of heating oil (regular and nontoxic) from three products (called distillates 1, 2, and 3) produced in the crude oil refining process. The distillates are purchased from a local refinery. The heating oils are simply blends of the three distillates, but must conform to certain specifications particularly with regard to their sulfur content and vapor pressure. The data for the heating oils are shown in Table 1 and the data for distillates is shown in Table 2. We assume that a blend of distillates has specifications (sulfur content, vapor pressure) equal to the weighted average of the components (this assumption is not in general true, for example, with octane rating.) Table 1: Heating-Oil Data Minimum Vapor Maximum Pressure Distillate 3 Content (%) 6 80 12 30 Maximum Sulfur Content (grams/barrel) 14 8 Selling Price ($/barrel) Maximum Monthly Sales (barrels) 10,000 4,000 Regular Nontoxic 12.00 16.00 Table 2: Distillate Data Vapor Pressure Cost (S/barrel) Sulfur Content (grams/barrel) 6 10 18 Distillate 1 Distillate 2 Distillate 3 16 Maximum Available (barrel/month) 3,000 2,000 10,000 10.00 14.00 6.00 8 4 The firm's objective is to determine how much of each distillate to combine (blend) in each heating oil so as to maximize profit. You are to set up the primal LP; you do not need to solve for a numeric solution