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
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Problem #1 – Product-Mix Problem**
Two-Tech Inc. is a small manufacturing firm producing two microwave components, known as Component A and Component B. The profit per unit of Component A is $20, whereas the profit per unit of Component B is $30.
Due to contractual commitments, Two-Tech must manufacture at least 25 units of Component A per week, and based on current demand, it can sell all units it manufactures. The objective is to **maximize profit** while operating within the following hourly constraints 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 quantity of each component to manufacture based on these limited resources. The decision variables are:
- \( X_1 \): amount of Component A manufactured per week
- \( X_2 \): amount of Component B manufactured per week
**Formulate and explain the mathematical model for this linear programming (LP) problem, including:**
a. **The Objective Function**
b. **All the constraints that the solution must satisfy, including nonnegativity.**
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