Related questions with answers

Question

Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3. A desk contributes $40 to profit, and a chair contributes$25. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. If 20 units of wood are available, formulate an LP to maximize Furnco’s profit. Then graphically solve the LP.

Solution

Verified
Step 1
1 of 5

Decision variables\text{\underline{\color{#4257b2}Decision variables}}

We will use x1=x_1 = number of desks, x2=x_2 = number of chairs.

Objective function\text{\underline{\color{#4257b2}Objective function}}

We must maximize the profit. This means that the objective function is

max z=40x1+25x2\max \ z = 40x_1 + 25x_2

Constraints\text{\underline{\color{#4257b2}Constraints}}

Constraint 1. The number of chairs must be at least twice the number of desks. Thus, we have x22x1x_2 \geqslant 2x_1, which can be written as 2x1x202x_1 - x_2 \leqslant 0. Constraint 2. Notice that x1x_1 desks and x2x_2 chairs require 4x1+3x24x_1 + 3x_2 units of wood. Therefore, 4x1+3x2204x_1 + 3x_2 \leqslant 20.

Sign restrictions\text{\underline{\color{#4257b2}Sign restrictions}}

Clearly x10x_1 \geqslant 0 and x20x_2 \geqslant 0.

Conclusion\text{\underline{\color{#4257b2}Conclusion}}

max z=40x1+25x22x1x204x1+3x220x1+.x20x20\begin{align*} \max \ z &= 40x_1 + 25x_2 \tag{Objective function}\\ 2x_1 - x_2 &\leqslant 0 \tag{Marketing restriction}\\ 4x_1 + 3x_2 &\leqslant 20 \tag{Wood restriction}\\ x_1 \phantom{+.x_2}&\geqslant 0 \tag{Sign restriction} \\ x_2 & \geqslant 0 \tag{Sign restriction} \end{align*}

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Recommended textbook solutions

Introduction to Operations Research 10th Edition by Frederick S. Hillier

Introduction to Operations Research

10th EditionISBN: 9780073523453Frederick S. Hillier
Verified solutions
Operations Research: Applications and Algorithms 4th Edition by Wayne L Winston

Operations Research: Applications and Algorithms

4th EditionISBN: 9780534380588Wayne L Winston
1,263 solutions
STAT: Behavioral Sciences 2nd Edition by Gary Heiman

STAT: Behavioral Sciences

2nd EditionISBN: 9781305436923Gary Heiman
A Mathematical Look at Politics 1st Edition by Daniel H. Ullman, E. Arthur Robinson Jr.

A Mathematical Look at Politics

1st EditionISBN: 9781439819838Daniel H. Ullman, E. Arthur Robinson Jr.

More related questions

1/2

1/3