Question

In: Finance

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.

Expert Solution

I have answered the question

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

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

A Furniture Company produces chairs and tables from two resources- labor and wood. The company has...

A Furniture Company produces chairs and tables from two resources- labor and wood. The company has 125 hours of labor and 45 board-ft. of wood available each day. Demand for chairs is limited to 5 per day. Each chair requires 7 hours of labor and 3.5 board-ft. of wood, whereas a table requires 14 hours of labor and 7 board-ft. of wood. The profit derived from each chair is $325 and from each table, $120. The company wants to determine...

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

The Pinewood Furniture Company produces chairs and tables from two resources, labor and wood. The company has 80 hours of labor and 36 pounds of wood available each day. Demand for chairs is limited to six per day. Each chair requires 8 hours of labor and 2 pounds of wood to produce, while a table requires 10 hours of labor and 6 pounds of wood. The profit derived from each chair is $400 and from each table, $100. The company...

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

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...

A furniture company produces tables (X) and chairs (Y). Available resources have indicated that the production...

A furniture company produces tables (X) and chairs (Y). Available resources have indicated that the production volume level should not exceed 1200 units per week and the demand for chairs is at most half of that for tables. Further, the production level of tables can exceed three times the production of chairs by at most 600 units. If the company makes a profit of OMR12 and OMR 16 per unit respectively on tables and chairs, how many of each should...

Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in...

Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of labor hours in the carpentry department and a certain number of labor hours in the painting department. Each table takes 3 hours of carpentry work, an hour and a half of assembly and 2 hours of finishing work. Each chair requires 4 hours of carpentry, and hour and 15 minutes of assembly and 1 hour of painting....

A company produces wooden chairs and tables. Each chair uses 10 lbs. of wood and takes...

A company produces wooden chairs and tables. Each chair uses 10 lbs. of wood and takes 10 hours to construct. Each table uses 15 lbs. of wood and takes 5 hours to construct. There are up to 150 lbs. of wood available and up to 110 labor hours available. If the profit on each chair is $3 and the profit on each table is 4$. We wish to maximize the profit. Let x be the number of chairs produced and...

Furniture Classics makes outdoor furniture from aged wood. The company’s primary product lines are chairs and...

Furniture Classics makes outdoor furniture from aged wood. The company’s primary product lines are chairs and tables. Below is data for the recent quarter: Chairs Tables Total Quantity sold 8,000 1,500 Revenue $800,000 $375,000 $1,175,000 Direct materials 288,000 140,625 428,625 Direct labor 192,000 46,875 238,875 Contribution margin $320,000 $187,500 $507,500 Traceable fixed costs 125,000 100,000 225,000 Allocated fixed costs 75,000 75,000 150,000 Profit before taxes $120,000 $12,500 $132,500 To encourage sales of tables, management is considering rewarding the salesperson who...

The Hickory Furniture Co. produces sofas and chairs. Their plant uses three main resources to make...

The Hickory Furniture Co. produces sofas and chairs. Their plant uses three main resources to make furniture –wood, upholstery and labor. The resource requirements and profits for each piece of furniture and the total resources available weekly are as follows: Sofa Chair Available Resource Wood (lbs) 7 4 1200 Upholstery (yds) 12 0 600 Labor (hrs) 6 10 400 Profit $500 $400 LINEAR PROGRAMMING (Hickory Furniture) __________ 1a. How many sofas should be produced? __________ 1b. How many chairs should...

A furniture manufacturer specializes in wood tables. The tables sell for $ 140 per unit and...

A furniture manufacturer specializes in wood tables. The tables sell for $ 140 per unit and incur $ 49 per unit in variable costs. The company has $ 14,560 in fixed costs per month. The company desires to earn an operating profit of $ 8,190 per month. (Abbreviation used; CM = contribution margin.) 10. Calculate the required sales in units to earn the target profit using the equation method. 11. Calculate the required sales in units to earn the target...

G&G Furniture Co. produces chairs and tables. The following table gives the profit generated per unit,...

G&G Furniture Co. produces chairs and tables. The following table gives the profit generated per unit, as well as the amount of wood, labor and other materials required, per unit of each product along with their maximum monthly limits in terms of availability. Chairs Tables Max Limits profit $100 $125 Wood 20 lbs per unit 30 lbs per unit 6000 lbs Other Materials 1 lbs per unit 1 lbs per unit 400 lbs Labor 1.5 hours per unit 2 hours...