Question

In: Statistics and Probability

Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each...

Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each chair requires 5 hours of labor (L) and 4 linear feet of rich mahogany (M), and each table requires 3 hours of labor and 20 linear feet of rich mahogany. The company has 240 labor hours available this week, and the warehouse has 700 linear feet of rich mahogany available. Profit for each chair is $150 and for each table is $750. At the optimal solution, how many tables should be produced? What is the maximum profit?

Expert Solution

Let be the number of chairs and be the number of tables manufactured. Then the LP problem is

The optimum occurs at the corners of the feasible region.

The corners are found below.

Solving together,

The other corners are .

The profit at is

Hence the optimal solution is chairs and tables. The maximum profit is .

orchestra answered 2 years ago

Cornell Corporation makes two products, chairs (C) and tables (T). The relationship between profit (PR), the...

Cornell Corporation makes two products, chairs (C) and tables (T). The relationship between profit (PR), the firm’s annual profit (in thousands of dollars), and its output of each good is: PR = -80 + 30C + 25T – 4C2 – 3T2 – 2CT Where C is the firm’s hourly output of chairs and T is the firm’s hourly output of tables. (Neither C nor T needs to be an integer.) a) Find the output of chairs and the output of...

THREE-PRODUCTS COMPANY MAKES AND SELLS THREE PRODUCTS: TABLES, CHAIRS, AND SHELVES. FOR EACH TABLE SOLD, THEY...

THREE-PRODUCTS COMPANY MAKES AND SELLS THREE PRODUCTS: TABLES, CHAIRS, AND SHELVES. FOR EACH TABLE SOLD, THEY SELL 6 CHAIRS AND 3 SHELVES. SELLING PRICES FOR TABLES, CHAIRS, & SHELVES ARE $50, $10, AND $15, RESPECTIVELY; WHILE THE VARIABLE COSTS ARE $40, $5, AND $7, RESPECTIVELY. THE TOTAL FIXED COSTS ARE $12,800. 1. CALCULATE THE BREAK-EVEN IN UNITS AND SALES-DOLLARS. 2. IF THE TAX-RATE IS 30% AND THE DESIRED AFTER-TAX PROFIT IS $4,480, WHAT IS THE TARGET SALES IN UNITS AND...

A furniture store manufactures 2 products; tables (X) and chairs (Y): the production process for each...

A furniture store manufactures 2 products; tables (X) and chairs (Y): the production process for each 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 and 2 hours of painting work. Each chair requires 4 hours of carpentry and 1 hour of painting. During the current month, 2,400 hours of carpentry time and 1,000 hours of painting time are...

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 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...

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 $50, and the profit for each chair is $40. 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...

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...

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) Problem Statement Montana wood products manufacture two high quality products, tables and chairs. Its profit...

(a) Problem Statement Montana wood products manufacture two high quality products, tables and chairs. Its profit is $15 per chair and $21 per table. Weekly production is constrained by available labor and wood. Each chair requires 4 labor hours and 8 board feet of wood, while each table requires 3 labor hours and 12 board feet of wood. Available wood is 2400 board feet and available labor is 920 hours. Management also requires at least 40 tables and at least...

Hillside Furniture Company makes outdoor furniture from recycled products, including plastics and wood by-products. Its three...

Hillside Furniture Company makes outdoor furniture from recycled products, including plastics and wood by-products. Its three furniture products are gliders, chairs with footstools, and tables. The products appeal primarily to cost-conscious consumers and those who value the recycling of materials. The company wholesales its products to retailers and various mass merchandisers. Because of the seasonal nature of the products, most orders are manufactured during the winter months for delivery in the early spring. Michael Cain, founder and owner, is dismayed...