Question: 1. ABC Company is introducing two new Car frames, the Deluxe and the Professional, to be made from aluminum and steel alloys. The expected unit

1. ABC Company is introducing two new Car frames, the Deluxe and the Professional, to be made from aluminum and steel alloys. The expected unit profits are SAR 30 for the Deluxe and SAR 50 for the Professional. The number of pounds of each alloy needed per frame is summarized in the following table. A supplier delivers 100 pounds of the aluminum alloy and 150 pounds of the steel alloy weekly. Table: Pounds of each alloy needed per frame Frame Aluminum Alloy Steel Alloy Deluxe 2 3 Professional 5 6 Formulate the above problem as linear programming problem. 2. Solve the following Linear Programming Problem by Graphical Method: Max z = 25x + 35x s.t., 5x +4x2 40 x + x 5 andx, x 20 3. Solve the following Linear Programming Problem by Mathematical Method: Max z = 5 x + 5x s.t., 3x + 6x 18 6x + 3x 18 andx, x 20 4. Solve the following Linear Programming Problem by Graphical Method: Min z = 5x + 2x S.L., 2x + 5x 2 10 4x + x 2 12 andx, x 20 5. Find the Range of Optimality for c and c2 of the following LPP. Max z 10x + 15x2 s.t., 3x1 + 4x2 10 2x1+ 5x28 and X1, X20

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