## Question:

## Answer:

### Introduction

The existence of long-term projections shows that an expected levels of demand of one hundred units of a particular product A and the alternative product B every day production capacity. There are constraints which can be considered as the upcoming limitations on producing the maximum expected capacity.

The number of units that can be produced cannot go beyond 200 units and 170 units of product B on a daily basis. The level of utility that is required to be met in order to satisfy the shipping of these goods is a total of at least 200 calculators capable of being delivered every day.”(Samuel, 2003) argued that Linear Programming 2: Theory and Extensions in Springer Series in Operations Research and Financial Engineering”.

Given that each unit of the scientific calculator that was supplied results to a $ 3 in loss made but every unit of B produced produce a $6 in profit made we can then determine the amount that the company can make daily in order to maximize the profits. X: stands for the units A produced while y: represents the units of B that were manufactured. In this perspective the company cannot produce a negative number of calculators hence there exists two constraints, x?0 and y=/0. However in this case the problem solver can ignore the constraints because x is represented by equal or greater than 100 and y is greater than or equal to 80.” (Fang, 1993)Linear Optimization and Extensions: Theory and Algorithms”.

This activity that was undertaken also led to a maximum: x_< 200 and y was given by the value less than or equal to 170. Combination that gives us the breakeven point where neither profit nor loss is made is x +y?200 hence this justifies the fact that y?-x + 200. The amount of profit that leads to the relationship will be the value that was optimized in the equation: P = -3X + 6Y.

In our second scenario the representation of the system will be given by the equation that is simplified as P= -3x + 6y, currently subject to: 100?x?200, also do consider the value 80?y?170 and finally the resulting solution is y?-x +200. “(Daniel, 1997) said that Linear Programming 1: Introduction, Springer Series in Operations Research and Financial Engineering”

Our feasibility region of the graph will be as follows resulting from the computation is as follows.

After the corners are put into a test there are points that are derived at (100,170), (200, 170), (200, 80), (120, 80) and (100, 100). The value that is obtainable as result of this sum is equal to P= 653 at (x, y) = (100, 170). The expected answer from the linear programming equation is 100 units of product A and 170 units of units B produced. In the above computation I have used the most optimal method to achieve the applicable and very best result. The lowest cost that was incurred in the production process has been depicted and also the highest level of profit attainable. The model has incorporated mathematics in the modules in getting the feasibility region. “Cook, (1997) said that Combinatorial Optimization of functions that are in linear programming”.

Objective that is referred to as the linear factor has been used in minimizing and increasing the inequality constraints. Simplex method could not be the suitable method because it results to confusion and alters the proposed path of the algorithms.

## References

Cook, W. (1997). The available combinatorial optimization of functions that are found in linear programming perspective. Winger man press. New York.

Fang, S. (1993). Linear Optimization and Extensions: Theory and Algorithms. Prentice press, Upper River town.

Daniel, K. (1997). Linear Programming 1: Introduction, Springer Series in Operations Research and Financial Engineering, springer press. New York.

Samuel, L. (2003). Linear Programming 2: Theory and Extensions in Springer Series in Operations Research and Financial Engineering, Springer press. New York.