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Sample Questions for the Final Exam Last Update: March 16, 2015 Problem 1 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 + 10x2 Subject to: 2x1 + 4x2≤40 x1+ x2≤15 x1 ≥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 + 6x2 Subject to: 4x1 +2x2≥20 -6x1 +4x2≤12 x1 +x2≥6 x1, x2≥0 3.Do the following LP problems have solutions? Why or why not? 3.1 Maximize: P = 300 x + 500y Subject to: 3x + 5y ≤30 x + y ≥18 x, y ≥0 1
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3.2 Maximize: P = 300x + 500y Subject to : x ≤18 y ≥2 x, y ≥0 4. 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? 5. The Pyrotec Company produces three electrical products – clocks, radios, and toasters. These products have the following resource requirements. Cost/Unit Labour hours/Unit Clock $7 2 Radio $10 3 Toaster $5 2 The manufacturer has a daily production budget of $2000 and a maximum of 660 hours of labour. Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios for $20 and toasters for $12. The company desires to know the optimal product mix that will maximize profit. Formulate a linear programming model for this problem. 2