The Whitt Window Company is a company with only three employees which makes two different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. They earn $60 profit for each wood-framed window and $30 profit for each aluminum-framed window. Doug makes the wood frames, and can make 6 per day. Linda makes the aluminum frames, and 4 per day. Bob forms and cuts the glass, and can make 48 square feet of glass per day. Each wood-framed window uses 6 square feet of glass and each aluminum-framed window uses 8 square feet of glass.

1. Determine the decision variables.

2. Determine the constraints.

3. Formulate a linear programming model.

4. Define:
a. Optimum solution
b. Optimum value
c. Slack variable
d. Range of Optimality
e. Range of Feasibility
f. Shadow Price
g. Binding Constraints
h. Non-binding constraints
i. Feasible Region

5. Transform the linear programming model in (3) to standard form.

6. Using graphical method, analyze the phrases defined in (4).

The decision variables are the number of wood-framed windows and the number of aluminum-framed windows. The constraints include Doug's production limit, Linda's production limit, and the available glass. A linear programming model is formulated to maximize profit, subject to the constraints.

1) Determine the decision variables.

The decision variables in this problem are the number of wood-framed windows (x) and the number of aluminum-framed windows (y) that the company should produce.

2) Determine the constraints.

The constraints are as follows:

Constraint 1: Doug can make 6 wood-framed windows per day.

So, the number of wood-framed windows (x) should be less than or equal to 6.

Constraint 2: Linda can make 4 aluminum-framed windows per day.

So, the number of aluminum-framed windows (y) should be less than or equal to 4.

Constraint 3: Bob can form and cut 48 square feet of glass per day.

Each wood-framed window uses 6 square feet of glass and each aluminum-framed window uses 8 square feet of glass.

So, the total square feet of glass used by the wood-framed windows (6x) and the aluminum-framed windows (8y) should be less than or equal to 48.

3) Formulate a linear programming model.

The linear programming model for this problem is:

Maximize profit: 60x + 30y

Subject to constraints: x ≤ 6, y ≤ 4, 6x + 8y ≤ 48

Non-negative constraints: x ≥ 0, y ≥ 0