Quiz_1_09F.docx

MGMT 306 ? Quiz 1, Fall 2009 Name: ID: ___________________________ Graphical Solution Method: Consider the following constraints and the corresponding graph below: Constraint 1: Constraint 2: Constraint 3: y x - 3 y = - 2 x + 2 y = 8 2 x - y = 1 1 0 5 3 2 6 4 1 7 0 2 3 4 7 6 5 x 8 (3 points) Shade the feasible region in the graph provided above. (3 points) The objective function is Maximize. Mark the optimal solution(s) in the above graph. Do not calculate the x and y coordinates at optimal solution(s). Draw the optimal objective function line through the optimal solution(s). (4 points) Linear Programming Formulation: Herman Johnson makes tables and chairs for sale in furniture specialty stores. Each table he makes yields a profit of $120 for him. Each chair generates a profit of $40. A table requires 40 square feet of lumber and takes Herman 8 hours to assemble. A chair requires 15 square feet of lumber and takes him 3 hours to assemble. Herman has 300 square feet of lumber and 40 labor hours available. Formulate a linear program to help Herman decide how many tables and chairs to build in order to maximize his profit. (Do not solve the problem.) Decision variables: T represents the number of tables that Herman builds. C represents the number of chairs that Herman builds. Objective function: Constraints: Quiz 1 Solution Problem 1. Feasible region: y o ptimal objective function line x + 2 y = 8 2 x - y = 1 1 0 5 3 2 6 4 1 7 0 2 3 4 7 6 5 x 8 optimal solution x - 3 y = - 2 Optimal solutions and optimal objective function line: The objective function line can be seen dashed in the graph. Problem 2. Objective function: Maximize 120T + 40C (weekly profit)Constraints: 40T + 15C < 300 8T + 3C < 40 T , C > 0. 3