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Problem 2 Woods products Ltd. currently produces two major products, tables and chairs. When sold, each chair yields a profit of Rs. 35 and table Rs. 45. An analysis of the production work sheets reveals the following manufacturing data: Product Man hrs. per unit Machine hrs. per unit Chair 0.8 Table 8 1.2 Time available during the year 800 Man Hours 485 Machine Hours The company has a minimum demand for 50 chairs and maximum demand for 25 tables during year 2003. Construct an appropriate linear program for maximizing the profit of Woods Product Ltd. Solution: Data Summary Chart Variable per Unit Man hrs. per Unit Machine hrs. per Demand (Units) 50 (min) 25 (max) Profit Unit Chairs 0.8 Rs.35 Tables 8 1.2 Rs.45 Resource Limits 800 (max) 485 (max) • Decision Variable: x, = Chairs x, = Tables • Objective Function: Maximize (z) = 35x, + 45x, • Constraints: Man Hour Constraints: 5x, + 8x, s 800 Machine Hour Constraints: 0.8x, + 1.2x, s 485 Demand Constraints: x, 2 50 X, 2 25 Non-Negativity: where x,, x, 2 0

Problem 2 Woods products Ltd. currently produces two major products, tables and chairs. When sold, each chair yields a profit of Rs. 35 and table Rs. 45. An analysis of the production work sheets reveals the following manufacturing data: Product Man hrs. per unit Machine hrs. per unit Chair 0.8 Table 8 1.2 Time available during the year 800 Man Hours 485 Machine Hours The company has a minimum demand for 50 chairs and maximum demand for 25 tables during year 2003. Construct an appropriate linear program for maximizing the profit of Woods Product Ltd. Solution: Data Summary Chart Variable per Unit Man hrs. per Unit Machine hrs. per Demand (Units) 50 (min) 25 (max) Profit Unit Chairs 0.8 Rs.35 Tables 8 1.2 Rs.45 Resource Limits 800 (max) 485 (max) • Decision Variable: x, = Chairs x, = Tables • Objective Function: Maximize (z) = 35x, + 45x, • Constraints: Man Hour Constraints: 5x, + 8x, s 800 Machine Hour Constraints: 0.8x, + 1.2x, s 485 Demand Constraints: x, 2 50 X, 2 25 Non-Negativity: where x,, x, 2 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the optimization problem using linear programming. Find the optimal solution with graph.

Problem 2 Woods products Ltd. currently produces two major products, tables and chairs. When sold, each chair yields a profit of Rs. 35 and table Rs. 45. An analysis of the production work sheets reveals the following manufacturing data: Product Man hrs. per unit Machine hrs. per unit Chair 0.8 Table 8 1.2 Time available during the year 800 Man Hours 485 Machine Hours The company has a minimum demand for 50 chairs and maximum demand for 25 tables during year 2003. Construct an appropriate linear program for maximizing the profit of Woods Product Ltd. Solution: Data Summary Chart Variable per Unit Man hrs. per Unit Machine hrs. per Demand (Units) 50 (min) 25 (max) Profit Unit Chairs 0.8 Rs.35 Tables 8 1.2 Rs.45 Resource Limits 800 (max) 485 (max) • Decision Variable: x, = Chairs x, = Tables • Objective Function: Maximize (z) = 35x, + 45x, Constraints: Man Hour Constraints: 5x, + 8x, s 800 Machine Hour Constraints: 0.8x, + 1.2x, s 485 Demand Constraints: x, 2 50 X, 2 25 Non-Negativity: where x,, x, 2 0
Transcribed Image Text:Problem 2 Woods products Ltd. currently produces two major products, tables and chairs. When sold, each chair yields a profit of Rs. 35 and table Rs. 45. An analysis of the production work sheets reveals the following manufacturing data: Product Man hrs. per unit Machine hrs. per unit Chair 0.8 Table 8 1.2 Time available during the year 800 Man Hours 485 Machine Hours The company has a minimum demand for 50 chairs and maximum demand for 25 tables during year 2003. Construct an appropriate linear program for maximizing the profit of Woods Product Ltd. Solution: Data Summary Chart Variable per Unit Man hrs. per Unit Machine hrs. per Demand (Units) 50 (min) 25 (max) Profit Unit Chairs 0.8 Rs.35 Tables 8 1.2 Rs.45 Resource Limits 800 (max) 485 (max) • Decision Variable: x, = Chairs x, = Tables • Objective Function: Maximize (z) = 35x, + 45x, Constraints: Man Hour Constraints: 5x, + 8x, s 800 Machine Hour Constraints: 0.8x, + 1.2x, s 485 Demand Constraints: x, 2 50 X, 2 25 Non-Negativity: where x,, x, 2 0
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