How do I solve this ## Linear Programming Problem### Problem StatementAn 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?### Tasksa. **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.

a Let x units of model A and y units of model B is ordered.b Then from the given condition we must…

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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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.

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