Assignment: Linear Programming
I. A furniture company is producing tables and chairs. The production of tables and chairs will go through two processes: wood cutting and assembly. In the wood cutting process, the required labor hour is 1 hour for a chair and 2 hours for a table. In the assembly process, the required labor hour is 4 hours for a chair and 3 hours for a table. For the coming week, the maximum labor hour is 70 hours for the wood cutting process and 180 hours for the assembly process. Based on the company's inventory level, the company decides to produce no more than 100 chairs and 30 tables for the coming week. Suppose the profit margin is $5/chair and $6/ table. Set up a linear programming model to maximize the total profit for this furniture company and solve the model using Excel Solver.
II. Identify the feasible region for the following set of constraints:
3x - 2y ≥ 0
2x - y ≤ 200
x ≤ 150
x,y≥ 0
III. Given the linear program
Max 3x + 4y
s.t. -x + 2y ≤ 8
x + 2y ≤ 12
2x + y ≤ 16
x , y ≥ 0
• Write the problem in standard form. Identify slack/surplus variables.
• Find all the extreme points. List the value for x and y at each extreme point.
• What is the optimal solution?
• What are the values of the slack/surplus variables at the optimal solution?
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