Module 2 - Optimization models

Introduction

This is a hand-in written by Group 60 (FIRE) for the weekly module #2 in the mathematical modelling course (DAT026) at Chalmers University of Technology.

Group 60 consists of:

  • Mazdak Farrokhzad

    • 901011-0279

    • twingoow@gmail.com

    • Program: IT

    • Time spent: x hours, y minutes

  • Niclas Alexandersson

    • 920203-0111

    • nicale@student.chalmers.se

    • Program: IT

    • Time spent: x hours, y minutes

We hereby declare that we have both actively participated in solving every exercise, and all solutions are entirely our own work.

Problem 1 - TVs and Profit

Description of the problem

The problem is about manufacturing TV devices and the profits of selling them.

We will briefly provide a summary of the problem using variables.

In this problem, all units manufactured are assumed to be sold. We also assume that the fixed cost of each device are separate so that they are separate in our expressions and functions, therefore we split the cost so that each TV model has half of the given fixed cost. From the provided description of the problem it is not obvious that this choice is wrong or right, it is a choice.

\(i\) \(i = 1\) \(i = 2\)
TV size, \(t_i\) \(t_0 = 19"\) \(t_1 = 21"\)
Retail selling price , \(r_i\) \(r_0 = 3390\) \(r_1 = 3990\)
Unit cost, \(u_i\) \(u_0 = 1950\) \(u_1 = 2250\)
Fixed cost, \(f_i\) \(f_0 = 2 \cdot 10^6\) \(f_1 = 2 \cdot 10^6\)
Price drop per unit sold \(d_i\) \(d_0 = 0.1\) \(d_1 = 0.1\)
Price drop per unit sold of other TV \(c_i\) \(c_0 = 0.03\) \(c_1 = 0.04\)
Units sold, \(s_i\) \(s_1\) \(s_2\)
Average selling price \(a_i\) \(a_1 = r_1 - d_1s_1 - c_1s_2\) \(a_2 = r_2 - d_2s_2 - c_2s_1\)