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: The Objective Function b. All the constraints that the solution must satisfy, including nonnegativity. a.
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: The Objective Function b. All the constraints that the solution must satisfy, including nonnegativity. a.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
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