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BSTA 450 - Review Sheet - Test 2 1. Consider the following linear programming problem: Maximize Z = 400 x + 100y Subject to 8 x + 10y ≤ 80 2 x + 6y ≤ 36 x≤ 6 x, y ≥ 0 BSTA 450 Find the optimal solution using the graphical method (use graph paper). Identify the feasible region and the optimal solution on the graph. How much is the maximum profit? Consider the following linear programming problem: Minimize Z = 3 x + 5 y (cost, $) subject to 10 x + 2 y ≥ 20 6 x + 6 y ≥ 36 y ≥ 2 x, y ≥ 0 Find the optimal solution using the graphical method (use graph paper). Identify the feasible region and the optimal solution on the graph. How much is the minimum cost? 2. The Turner-Laberge Brokerage firm has just been instructed by one of its clients …show more content…

Each ingredient contains the same three antibiotics in different proportions. One gram of ingredient 1 contributes 3 units, and ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of antibiotic 2 are required, and the ingredients each contribute 1 unit per gram. At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is $50. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost. Formulate a linear programming model for this problem. Consider the following linear programming problem: Maximize Z = 300 x1 + 500 x2 7. subject to : 3x1 + 5 x2 ≤ 30 x1 + x2 ≥ 18 x1 , x2 ≥ 0 Why this problem has no solution? Definitions and concepts to know 1. 2. 3. 4. 5. 6. 7. 8. 9. Decision variable Objective function Constraint Feasible region Isoprofit line Isocost line Unboundedness Infeasibility Maximization problem 10. Minimization problem 11. Redundant constraint 12. Alternate optimal solutions 13. Binding constraint 14. Slack value 15. Corner point method 16. Classical problems: a. the marketing problem b. the investment problem c. the blend problem d. the product mix problem e. the transportation

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