Mathematical Concepts and Scenarios

Introduction

Mathematical concepts and scenarios have been around for thousands of years. Math makes everyday life easier and provides a clearer picture to more complex situations. Technology such as cell phones, computers, and Google all use mathematical data, including matrices, to better serve society. The simplex method is a common method to develop an optimal solution to a problem. The business world requires efficiency to lower costs and increase production to achieve a maximum profit. This makes the simplex method a perfect solution to everyday business needs to assist in creating profit. A company can produce 100,000lbs a day and it has 3 items it can produce. These items include Item A, B, and C. Item A has a 10% profit, Item B has a 7% profit and Item C has a 9% profit. The total production of Item A cannot exceed total production of B & C. How much production should be run for each item? What is the maximum profit? All of these difficult questions will be answered using the simplex method with a few simple steps.

Conclusion

After being presented a problem with the company to produce 100,000 pounds a day, it's apparent that the simplex solution provides the company with the best opportunity to maximize profit while minimizing labor and costs. The maximum profit will be 9500 if produced at 100 percent efficiency. The company will need to produce 50,000 pounds of product A and 50,000 pounds of product C. The initial problem stated that product A cannot exceed the total of products B and C. It does not exceed total production of the two but it is equal to the amount produced. It is not profitable to produce Item B as it only provides a 7% profit as opposed to a 9% and a 10% profit. Therefore the optimal solution is: p = 9500; x1 = 50000, x2 = 0, x3 = 50000 Maximize p = .10x1 + .07x2 + .09x3 subject to x1 + x2 + x3 <= 100000 x1 - x2 - x3 <= 0.