Scenario

Due to the spread of Covid19 around the world in early 2020, many countries adopted online learning. There was a spike in computer sales after many years of sluggish growth.

Megabyte Computers WLL decided to exploit this opportunity to introduce new laptop models for students: STANDARD for school students and TURBO for university students. The STANDARD computer production line can produce, at most, 50 computers per day. At the same time, the TURBO computer production line can turn out 60 computers per day. The factory has only 80 hours of daily labour. STANDARD computers require 0.5 hour of labour, while TURBO computers require 1 hours of labour. Megabyte Computers can sell every STANDARD unit it produces for a profit contribution of BD 40, and each TURBO unit for a contribution of BD 60.

The problem for Megabyte Computers is to determine the mix of STANDARD and TURBO computers to produce each day to maximize total profit without exceeding line and labour capacity limits.

Task 1: Discuss the type of this operational problem and identify the decision variables and objective function.

Task 2: Create a resource-activities allocation table and write the mathematical model in standard form.

Task 3: Apply at least 10 steps using the try-and-error method to find feasible solutions. Initiate your solution by assigning zero to decision variables. In other steps, justify your choice of values for the decision variables.

Task 4: Apply the graphical method to obtain an optimal solution.

Task 5: Convert the standard model of Task 2 to the matrix form.

Task 6: Convert the standard model of Task 2 to the augmented form.

Task 7: Convert the augmented form to the tabular form (Simplex Table).

Task 8: Using the Simplex table created in Task 7, apply the simplex method to obtain an optimal solution. List the steps to reach an optimal solution.

Task 9:

- Use LINGO or Excel Solver to obtain an optimal solution with the simplex method.

- Determine the allowable range of the model parameters.

- Show and discuss the results

Task 10: Assume you are a member of the Operations Research team at Megabyte Computers. You have found the solution and you need to present it to top management. Present your Simplex and LINGO/Excel results in a language suitable to the top management. 2-3 power points slides might be adequate.