IE311: Operations Research Assignment 1: (Introduction to Linear Programming - Part 1: Graphical method) Due Date: Wednesday 16/9/2020 Problem 1 The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a suf of redwood for use in the furniture. During the next production cycle, 1,800 hours of labor are available under a union agreement. The firm also has a stock of 3,000 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 6 labor hours and 12 feet of redwood; each picnic table takes 10 labor hours and 15 feet of redwood. Completed benches will yield a profit of $25 each, and tables will result in a profit of $35 each. a) Formulate the problem as an LP model to maximize profit. b) Illustrate the feasible region graphically. c) Use the corner point graphical method to find the optimal solution. Problem 2 Consider the following LP problem: Maximize Z= 2X + 2Y subject to 2x + 5Y