Question

A division of the Winston Furniture Company manufactures dining tables and chairs. Each table requires 40...

A division of the Winston Furniture Company manufactures dining tables and chairs. Each table requires 40 board feet of wood and 3 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. The profit for each table is $40, and the profit for each chair is $30. In a certain week, the company has 3200 board feet of wood available and 520 labor-hours available. How many tables and chairs should Winston manufacture to maximize its profit? (Let x represent the number of tables Winton manufactures and let y represent the number of chairs they manufacture.)

(x, y) =

What is the maximum profit? $

Homework Answers

Answer #1

Let x and y represent the number of tables and chairs manufacture by Winton respectively.

Now x tables will require 40x board feet of wood and 3x labor-hours and y chairs will require 16y board feet of wood and 4y labor-hours. Now, since, the company has 3200 board feet of wood available and 520 labor-hours available, hence 40x+16y ≤ 3200 or, 5x+2y ≤ 400…(1) and 3x+4y ≤ 520…(2)

Further, the profit for each table is $40, and the profit for each chair is $30 so that Winton’s profit for the week is P(x,y) = 40x+30y.

A graph of the lines y = -(5/2)x +200 ( in red) and y = -(3/4)x+130 ( in blue) is attached. The feasible region is on and below both these lines. The 2 lines intersect at the point (40,100) so both the conditions (1) and (2) are satisfied when x = 40 and y = 100.

Thus, the maximum profit will be $ (40*40+30*100) = $ 4600.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table...
A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 3 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. In a certain week, the company has 3200 board feet of wood available and 520 labor-hours. If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits...
❑A furniture Company produces tables and chairs. Each table takes four hours of labor from the...
❑A furniture Company produces tables and chairs. Each table takes four hours of labor from the carpentry department and two hours of labor from the finishing department. Each chair requires three hours of carpentry and one hour of finishing. During the current week, 260 hours of carpentry time are available and 120 hours of finishing time. Each table produced gives a profit of $60 and each chair a profit of $40. How many chairs and tables should be made? 1....
4) A furniture manufacturing company manufactures tables and chairs. The relevant manufacturing data are given in...
4) A furniture manufacturing company manufactures tables and chairs. The relevant manufacturing data are given in the table below. How many tables and chairs should be manufactured each day to maximize profit? (12 POINTS) Note: Please clearly define your variables and indicate the objective function and the constraints. Indicate the scale of your axes, and write your final answer using a complete sentence with correct units. Department Table Labor-Hours per Unit Chair Labor-Hours per Unit Maximum Labor-Hours Available per Day...
A furniture company manufactures desks and chairs. Each desk uses four units of wood, and each...
A furniture company manufactures desks and chairs. Each desk uses four units of wood, and each chair uses three units of wood. A desk contributes $400 to profit, and a chair contributes $250. • Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. There are 2000 units of wood available. a. What are the decision Variables? B. what is the objective function? C. What are the constraints? D. Use Solver to...
Suppose that a furniture manufacturer makes​ chairs, sofas, and tables. Consider the following chart of labor...
Suppose that a furniture manufacturer makes​ chairs, sofas, and tables. Consider the following chart of labor hours required and available. Chair Sofa Table Daily labor available​ (labor- hours) Carpentry 6 3 8 720 Finishing 1 1 2 144 Upholstery 4 6 0 320 The profit per chair is ​$70​, per sofa ​$50​, and per table ​$100. How many pieces of each type of furniture should be manufactured each day to maximize the​ profit?
The Outdoor Furniture Corporation manufactures two​ products, benches and picnic​ tables, for use in yards and...
The Outdoor Furniture Corporation manufactures two​ products, benches and picnic​ tables, for use in yards and parks. The firm has two main​ resources: its carpenters​ (labor force) and a supply of redwood for use in the furniture. During the next production​ cycle, 980 hours of labor are available under a union agreement. The firm also has a stock of 4,500 board feet of quality redwood. Each bench that Outdoor Furniture produces requires 4 labor-hours and 12 board feet of​ redwood;...
Question 3: Brown Company manufactures wood tables. Each table requires 15 board-feet of wood. Wood costs...
Question 3: Brown Company manufactures wood tables. Each table requires 15 board-feet of wood. Wood costs $6 per board foot. The company had 2,000 board feet wood on hand at the beginning of July and required enough wood inventory to be on hand to meet 20% of the following month’s production requirements. July August September Quarter Required Production 5,000 7,000 10,000 22,000 The company expects to produce 8,000 units in October. Required: Prepare a materials purchases budget for the quarter....
Part 3 – Steelcase Production Steelcase Corporation manufactures 3 basic products: chairs, desks, and tables. Below...
Part 3 – Steelcase Production Steelcase Corporation manufactures 3 basic products: chairs, desks, and tables. Below is chart which summarizes the number of labor hours spent for each product in each division. Chairs Desks Tables Process Carpentry 2 3 6 Finishing 1 1 1 Assembly 4 6 2 In a given week, Steelcase has 250 hours available for carpentry, 100 hours available for finishing, and 400 hours available for assembly. Steelcase makes a profit of $66 on each chair, $75...
Use below information for Questions 14 to 15: Company X produces dining chairs and tables. The...
Use below information for Questions 14 to 15: Company X produces dining chairs and tables. The following budget information is available: Item                                   Dining Chairs                    Tables                                Total Cost Machine Setups                             250                       600                                     TL48,100             Inspections                                      250                       470                                    TL72,000                            Labor hours                                     2,100                   2,410 Q-14) Compute total machine setups and inspection costs assigned to Dining Chairs, using plantwide method if the allocation base is labor hours. Q-15) Compute total machine setups and inspection...
10) Natural Furniture Company manufactures three outdoor products, chairs, benches, and tables. Each product must pass...
10) Natural Furniture Company manufactures three outdoor products, chairs, benches, and tables. Each product must pass through the following departments before it is shipped: sawing, sanding, assembly, and painting. The time requirements (in hours) are summarized in the tables below. The production time available in each department each week and the minimum weekly production requirement to fulfill contracts are as follows: Minimum Capacity Production Department (In Hours) Product Level Sawing 450 Chairs 100 Sanding 400 Benches 50 Assembly 625 Tables...