The Whitt Window Company is a company with only three employees that makes two different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. They earn a $60 profit for each wood-framed window and a $30 profit for each aluminum-framed window. Doug makes the wood frames and can make at most 6 per day. Linda makes the aluminum frames and can make at most 4 per day. Bob forms and cuts the glass and can make at most 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. The company wishes to determine the number of windows of each type to produce per day to maximize total profit.

(a) Formulate a linear programming model for this problem.

(b) Use the graphical method to solve the problem.

This question is a linear programming problem, where mathematical model is created to solve for maximum profit that can be achieved per day by considering constraints on manufacturing wood-framed and aluminium-framed windows. The constraints are determined by capacity of employees. This problem is best solved using a graphical method approach.

Explanation:

Let's start solving the problem step by step.

Step 1: Define the Decision Variables. Let 'X' be the number of wood-framed windows and 'Y' be the number of aluminum-framed windows.

Step 2: Define the Objective Function. The company wants to maximize profit, which is obtained by selling wood and aluminum windows. So, the objective function is 60*X + 30*Y.

Step 3: Define the Constraints. Doug can make at most 6 wood windows a day (X ≤ 6), Linda can make at most 4 aluminum windows per day (Y ≤ 4). Bob can handle at most 48 square feet of glass a day which equates to the constraints 6*X + 8*Y ≤ 48.

(b) To solve this problem graphically you need to plot these inequalities on a graph, the feasible region is the region that satisfies all these conditions.

Finally, find the corner points of this region, and substitute these values in objective function to find max profit.

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