Operations Management

1. Find the feasible region and optimum solution for this linear programming model, using the graphical method. What is the maximum profit?Maximize Z = 6.5x1 + 10x2Subject to:2x1 + 4x2 = 40x1 + x2 = 15x1 = 8 x1, x2 = 02. Find the feasible region and optimum solution for this linear programming model, using the graphical method. What is the minimum cost?Minimize Z = 8x1 + 6x2Subject to:4x1 +2x2 = 20-6x1 +4x2 = 12x1 +x2 = 6 x1, x2 = 03. Do the following LP problems have solutions? Why or why not?3.1 Maximize: P = 300 x + 500ySubject to:3x + 5y = 30x + y = 18x, y = 023.2 Maximize: P = 300x + 500ySubject to :x = 18y = 2x, y = 04. A jewellery store makes necklaces and bracelets from gold and platinum. The store has 18 ounces of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2 ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. The demand for bracelets is no more than four. A necklace earns $300 in profit and a bracelet, $400. The store wants to maximize profit. a) Formulate a linear programming model for this problem. b) Find the feasible region and optimum solution for this linear programming model, using the graphical method. What is the maximum profit? 



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