Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
5. Solve the following linear programming problem. An assistant manager of an appliance store is in charge of ordering two types of stereo systems. Model A costs $300 while Model B costs $400. The manager must order a total of at least 100 systems to meet demand. The store will make $40 on each model A system and $60 on each model B system and expects to make at least $4800 in total profit. How many of each model should be ordered in order to minimize the cost? a. Define your variables. b. Write the objective equation that represents the Cost (C). c. Write a system of all constraints for this problem. d. Solve the problem using the graph below. Be sure to locate all vertices and show your tests.

5. Solve the following linear programming problem. An assistant manager of an appliance store is in charge of ordering two types of stereo systems. Model A costs $300 while Model B costs $400. The manager must order a total of at least 100 systems to meet demand. The store will make $40 on each model A system and $60 on each model B system and expects to make at least $4800 in total profit. How many of each model should be ordered in order to minimize the cost? a. Define your variables. b. Write the objective equation that represents the Cost (C). c. Write a system of all constraints for this problem. d. Solve the problem using the graph below. Be sure to locate all vertices and show your tests.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

How do I solve this

## Linear Programming Problem ### Problem Statement An assistant manager of an appliance store is in charge of ordering two types of stereo systems. Model A costs $300 while Model B costs $400. The manager must order a total of at least 100 systems to meet demand. The store will make $40 on each Model A system and $60 on each Model B system and expects to make at least $4800 in total profit. How many of each model should be ordered in order to minimize the cost? ### Tasks a. **Define Your Variables** - Let \( x \) be the number of Model A systems ordered. - Let \( y \) be the number of Model B systems ordered. b. **Write the Objective Equation that Represents the Cost (C)** - The objective is to minimize the cost: \( C = 300x + 400y \). c. **Write a System of All Constraints for This Problem** - The total number of systems must be at least 100: \( x + y \geq 100 \). - The total profit must be at least $4800: \( 40x + 60y \geq 4800 \). - Non-negativity constraints: \( x \geq 0 \), \( y \geq 0 \). d. **Solve the Problem Using the Graph Below** - Be sure to locate all vertices and show your tests. ### Graph Explanation - A grid is provided to plot the constraints and identify feasible regions. - The axes represent the number of Model A (x-axis) and Model B (y-axis) systems. - Intersection points of the constraints will form vertices of the feasible region, which need to be evaluated to find the minimum cost.
Transcribed Image Text:## Linear Programming Problem ### Problem Statement An assistant manager of an appliance store is in charge of ordering two types of stereo systems. Model A costs $300 while Model B costs $400. The manager must order a total of at least 100 systems to meet demand. The store will make $40 on each Model A system and $60 on each Model B system and expects to make at least $4800 in total profit. How many of each model should be ordered in order to minimize the cost? ### Tasks a. **Define Your Variables** - Let \( x \) be the number of Model A systems ordered. - Let \( y \) be the number of Model B systems ordered. b. **Write the Objective Equation that Represents the Cost (C)** - The objective is to minimize the cost: \( C = 300x + 400y \). c. **Write a System of All Constraints for This Problem** - The total number of systems must be at least 100: \( x + y \geq 100 \). - The total profit must be at least $4800: \( 40x + 60y \geq 4800 \). - Non-negativity constraints: \( x \geq 0 \), \( y \geq 0 \). d. **Solve the Problem Using the Graph Below** - Be sure to locate all vertices and show your tests. ### Graph Explanation - A grid is provided to plot the constraints and identify feasible regions. - The axes represent the number of Model A (x-axis) and Model B (y-axis) systems. - Intersection points of the constraints will form vertices of the feasible region, which need to be evaluated to find the minimum cost.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS