Problem #1- A Product-Mix Problem Two-Tech Inc. is a small manufacturing firm and produces two microwave components, known as Component A and Component B. The profit per unit of the Component A is $20, whereas the profit per unit of Component B is $30. Because of contractual commitments, Two-Tech must manufacture at least 25 units of Component A per week, and based on the present demand for its products, it can sell all that it can manufacture. However, it wishes to maximize profit while operating the production department within the following availability of hours in the Assembly and Testing departments: Assembly hours: 240 hours available Testing hours: 140 hours available per week per week Component A requires 4 hours of assembly and 1 hour of testing, while Component B requires 3 hours and 2 hours, respectively. The problem is to determine the optimal number each component to manufacture based on the limited resources available. The decision variables directly under Two-Tech's control are: X1: amount of Component A manufactured per week X2: amount of Component B manufactured per week Formulate and explain the mathematical model for this LP problem, including:
Problem #1- A Product-Mix Problem Two-Tech Inc. is a small manufacturing firm and produces two microwave components, known as Component A and Component B. The profit per unit of the Component A is $20, whereas the profit per unit of Component B is $30. Because of contractual commitments, Two-Tech must manufacture at least 25 units of Component A per week, and based on the present demand for its products, it can sell all that it can manufacture. However, it wishes to maximize profit while operating the production department within the following availability of hours in the Assembly and Testing departments: Assembly hours: 240 hours available Testing hours: 140 hours available per week per week Component A requires 4 hours of assembly and 1 hour of testing, while Component B requires 3 hours and 2 hours, respectively. The problem is to determine the optimal number each component to manufacture based on the limited resources available. The decision variables directly under Two-Tech's control are: X1: amount of Component A manufactured per week X2: amount of Component B manufactured per week Formulate and explain the mathematical model for this LP problem, including:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve using MS Excel Solver
Transcribed Image Text:Problem #1-
A Product-Mix Problem
Two-Tech Inc. is a small manufacturing firm and produces two microwave components, known as
Component A and Component B. The profit per unit of the Component A is $20, whereas the profit per
unit of Component B is $30.
Because of contractual commitments, Two-Tech must manufacture at least 25 units of Component A per
week, and based on the present demand for its products, it can sell all that it can manufacture. However,
it wishes to maximize profit while operating the production department within the following availability
of hours in the Assembly and Testing departments:
Assembly hours: 240 hours available per week
Testing hours: 140 hours available per week
Component A requires 4 hours of assembly and 1 hour of testing, while Component B requires 3 hours
and 2 hours, respectively.
The problem is to determine the optimal number each component to manufacture based on the limited
resources available. The decision variables directly under Two-Tech's control are:
X1: amount of Component A manufactured per week
X2: amount of Component B manufactured per week
Formulate and explain the mathematical model for this LP problem, including:
a. The Objective Function
b. All the constraints that the solution must satisfy, including nonnegativity.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
