Chapter 2-An Introduction to Linear Programming & Graphical method1. Consider the following linear programming problemMax8X + 7Ys.t.15X + 5Y ? 7510X + 6Y ? 60X + Y ? 8X , Y ? 0a.Use a graph to show each constraint and the feasible region.b.Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?c.What is the optimal value of the objective function?2. For the following linear programming problem, determine the optimal solution by the graphical solution methodMax?X + 2Ys.t. 6X ? 2Y ? 3?2X + 3Y ? 6 X + Y ? 3 X , Y ? 03. Use this graph to answer the questions.Max20X + 10Ys.t.12X + 15Y ? 18015X + 10Y ? 1503X ? 8Y ? 0X , Y ? 0a.Which area (I, II, III, IV, or V) forms the feasible region?b.Which point (A, B, C, D, or E) is optimal?c.Which constraints are binding?d.Which slack variables are zero?4. Find the complete optimal solution to this linear programming problem.Min5X + 6Ys.t.3X + Y ? 15X + 2Y ? 123X + 2Y ? 24X , Y ? 05. And the complete optimal solution to this linear programming problem.Max5X + 3Ys.t.2X + 3Y ? 302X + 5Y ? 406X ? 5Y ? 0X , Y ? 06. Find the complete optimal solution to this linear programming problem.Max2X + 3Ys.t.4X + 9Y ? 7210X + 11Y ? 11017X + 9Y ? 153X , Y ? 07. Find the complete optimal solution to this linear programming problem. ...

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