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5. The Pinewood Furniture Company produces chairs and tables from two resources—labor and wood. The company...

5. The Pinewood Furniture Company produces chairs and tables from two resources—labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day to maximize profit.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.

Taylor, Bernard W., III. Introduction to Management Science (What's New in Operations Management) (p. 64). Pearson Education. Kindle Edition.

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Answer:

Profit per chair = $400

Profit per table = $100

Labor hours required to make a chair = 8 hours

Labor hours required to make a table = 10 hours

Wood used per chair = 2 board-ft

Wood used per table = 6 board-ft

Availability labor hours = 80 hours

Availability of wood = 36 board-ft.

Daily demand of chairs is limited to = 6 chairs per day

a.

Formulate the linear programming model for the problem as shown below:

Let x and y represent chair and table respectively.

b)

Solve the model using graphical analysis as shown below:

Step 1: Determine the solution for each equation by removing the inequality and putting equal to sign as shown below:

Equation 1:

This means y will stay zero in every case.

The graph of the equation in such case remains parallel to axis corresponding to variable having a constant value.

Equation 2:

Assume x and y zero in two different cases and find the value:

Equation 3:

Assume x and y zero in two different cases and find the value:

The coordinates and the value of objective function are as follows:

It can be observed that the highest value is at point C i.e. 2,720 which means the furniture company should make 6 chairs and 3.2 tables to maximize its profit.

jeff jeffy answered 1 year ago

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