# Linear Programming Production Line

That polygon may have an infinite number of edges, as long as they are all straight lines.) You are asking a max problem. So you want to find all the vertices of the feasible region. Then you evaluate the object function at each of them to see which one gives the largest value. One vertex is (0, 0). That one is easy. Can you find the other vertices? How much money will you make at each of them? Which one is the largest? What is the maximum profit? In summary, the problem is to maximize profit given the constraints of 480 minutes of skilled labor and 2,000 minutes of machine use, while producing a
I have absolutely no ides where to go from here, I am horrible at this, If you could help me I would appreciate it, I want help doing it, not just answers.

## Homework Statement

You are the owner of a manufacturing plant. We've been hired by Apple to produce iPhone and iPods. Apples pays us $50 for every iPhone and$30 for every iPod. The constraints are that I only have 480 minutes of skilled labor and 2,000 minutes of machine use.

The iPhones require 2 minutes of skilled labor and 6 minutes of machine use time.
The iPods require 1 minute of skilled labor, and 10 minutes of machine use time.

In TOTAL, I can only make 250 unitsP= Profit
A= iPhone
B= iPod

## The Attempt at a Solution

a = 2(skilled) + 6(machine) + 50(profit)
b = 1(skilled) + 10(machine) + 30(profit)

Last edited:
I have absolutely no ides where to go from here, I am horrible at this, If you could help me I would appreciate it, I want help doing it, not just answers.

## Homework Statement

You are the owner of a manufacturing plant. We've been hired by Apple to produce iPhone and iPods. Apples pays us $50 for every iPhone and$30 for every iPod. The constraints are that I only have 480 minutes of skilled labor and 2,000 minutes of machine use.

The iPhones require 2 minutes of skilled labor and 6 minutes of machine use time.
The iPods require 1 minute of skilled labor, and 10 minutes of machine use time.

In TOTAL, I can only make 250 units

P= Profit
A= iPhone
B= iPod
Much better to write full sentences in order to be clear and precise. I presume that what you mean is that you can make P dollars if you make A iphones and B ipods.

## The Attempt at a Solution

a = 2(skilled) + 6(machine) + 50(profit)
b = 1(skilled) + 10(machine) + 30(profit)
Again, you haven't defined your terms. Are "a" and "b" the same as "A" and "B"? If so that makes no sense. Those numbers look like the numbers given in how many minutes are required to make an iPhone or iPod. But then those are NOT equations. It looks like you are multiplying "2" by "skilled" and that is meaningless. And you certainly cannot add "minutes" and "dollars".

Let A be the number of iPhones made and let B be the number of iPods made. How much money would you make? That is the "object function".

How many minutes of skilled labor would be required? That must be larger than or equal to 0 and less than or equal to 480.

How many minutes of machine time would be required? That must be larger than or equal to 0 and less than or equal to 2000.

The total number of units made, A+ B, must be greater than or equal to 0 and less than or equal to 250.

The two inequalities define your "feasible region". The basic theorem of Linear programing is that max or min of a linear object function occur at the vertices of a convex polygonal feasible region.

The objective function would be: P = 50A + 30B

The constraints would be:
2A + B ≤ 480 (skilled labor constraint)
6A + 10B ≤ 2000 (machine use constraint)
A + B ≤ 250 (total unit constraint)

To solve this linear programming problem, you can use the simplex method or a graphing calculator. The optimal solution would be to produce 200 iPhones and 50 iPods, resulting in a profit of \$12,500. This solution satisfies all of the constraints and maximizes the profit.

In order to improve production efficiency or increase profit, you could also consider adjusting the production mix or investing in more skilled labor or machines. It is important to regularly analyze and optimize the production line to ensure maximum efficiency and profitability.

## What is linear programming in the context of production line optimization?

Linear programming is a mathematical technique used to optimize systems with several constraints and variables. In the context of production line optimization, it involves finding the most efficient way to allocate resources and maximize output while considering factors such as time, cost, and capacity.

## What are the main benefits of using linear programming in production line management?

Some of the main benefits of using linear programming in production line management include increased efficiency, cost reduction, improved resource allocation, and better decision-making. It can also help identify bottlenecks and optimize production processes.

## What type of problems can linear programming be used to solve in a production line?

Linear programming can be used to solve a variety of problems in production line management, such as production planning, inventory management, scheduling, and capacity planning. It can also be used to optimize supply chain management and distribution networks.

## What are the key steps in implementing linear programming in a production line?

The key steps in implementing linear programming in a production line include defining the problem, setting objectives and constraints, formulating a mathematical model, solving the model using appropriate algorithms, and interpreting the results to make decisions and adjustments as needed.

## What are some common challenges when using linear programming in production line optimization?

Some common challenges when using linear programming in production line optimization include data availability and accuracy, model complexity, and the need for specialized skills and software. It is also essential to regularly update and adapt the model to changing production and market conditions.

Replies
1
Views
771
Replies
2
Views
4K
Replies
6
Views
2K
Replies
17
Views
2K
Replies
4
Views
4K
Replies
1
Views
1K
Replies
3
Views
1K
Replies
1
Views
567
Replies
13
Views
5K
Replies
11
Views
2K