1. Linear Programming Wyndor Glass Co. 3 plants 2 new products
Product 1: glass door with aluminum framing
Product 2: 4x6 foot wood frame window

2. Wyndor Glass Problem cont.
Objective:
Determine what the production rates should be for the two products in order to maximize their total profit, subject to the restrictions imposed by the limited production capacities at each plant.

3. Wyndor Glass Problem cont.
Optimal Solution:
Product 1 – 2 batches/week
Product 2 – 6 batches/week
Profit - $36,000

4. Intro. To Linear Programming
Definition: Programming Problems
Concerned with the use or allocation of scarce resources (labor, materials, machines, and capital), in the “best” possible manner so that costs are minimized or profit is maximized.

5. Intro. To Linear Programming
Definition: Linear Programming Problems
The decision variables are non-negative
The objective function is linear
The constraint set is a set of linear equations
Other programming problems:
Integer
Non-linear (quadratic)
Goal
Paramteric

6. Why wide use of Linear Programming?
Wide variety of problems can be represented by an LP.
There exist efficient techniques for solving LPs.
Ease of analysis of data variation (sensitivity analysis)

7. Formulation of LP Model
Identify the decision variables.
Identify the problem constraints and express the constraints as a series of linear equations.
Identify the objective functions as a linear equation, and state whether the objective is maximization or minimization.

8. Formulation of Wyndor Glass Model
Identify the decision variables.
x1 – Number of batches of product 1 produced per week.
x2 – Number of batches of product 2 produced per week.
Identify the problem constraints and express the constraints as a series of linear equations.
Identify the objective functions as a linear equation, and state whether the objective is maximization or minimization.

9. Formulation of Wyndor Glass Model cont.