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Phase II) Building linear programming models
Session 3: Introduction to linear programming
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Transcript

Session 3: Introduction to linear programming

Phase II) Building linear programming models

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A simple example

The Glickman Electronics produces two products: x-pod and BlueBerry. To produce these products, they need:

  • Electronic work: each x-pod: 4 hours, each Blueberry: 3 hours
  • Assembly work: each x-pod: 2 hours, each Blueberry: 1 hour
During the current production period, 240 hours of electronic time and 100 hours of assembly time are available.
  • Each x-pod yields a profit of $7;
  • Each BlueBerry yields a profit of $5;

A simple example

The table below summarizes the info

Goal: determine the number of X-Pods and Blueberrys to produce to maximize the profit

Read the previous example carefully. Once you are ready, click on Start to answer some questions

Start

Go back

An employer suggested to produce 25 X-PODS and 50 BLUEBERRYS. What do you think about this suggestion?

It is a good idea

Question 1/3

It is possible but not a good idea

It is impossible to implement it

Next question

Well Done !

Indeed the solution requires more electronic work than available.

πŸ‘Ž

The solution does not satisfy the constraint regarding the electronic work

These solutions are called "infeasible"

X-PODS have a higher profit. If the firm only produces X-PODS, how much profit it can earn?

$ 350

Question 2/3

$ 420

$ 700

Next question

Well Done !

If the firm only produces X-PODS, it can produce a maximum of 50 X-PODS based on the assembly constraint.

πŸ‘Ž

Profit = 50 * 7 = $ 350

Is it a good idea to only produce X-PODS because they have a higher profit?

No, the firm can earn a higher profit by also producing Blueberrys

Question 3/3

Yes, it is the best thing to do

Well Done !

Based on Question 2, producing only X-PODS gives a profit of $350

πŸ‘Ž

You can easily verify that producing 40 X-PODS and 20 Blueberrys is feasible and gives a profit of $380

BUT! Can the company still do better? What is the optimal number of X-PODS and BlueBerrys? (You will see the answer later)

Try again!

Oops, not correct

Are you sure that the company has enough resources to implement the solution?

πŸ‘Ž

Try again!

Oops, not correct

Pay attention to both constraints. They determine the maximum X-PODS that the firm can produce

πŸ‘Ž

Try again!

Oops, not correct

What if the company reduces the number of X-PODS to 40 and then produce as much BlueBerrys as possible? Try it

πŸ‘Ž

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