International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 02 Issue: 01 | Apr-2015 www.irjet.net p-ISSN: 2395-0072 © 2015, IRJET.NET- All Rights Reserved Page 261 Linear Programming based Optimum Resource Utilization for Manufacturing of Electronic Toys Salma Shaheen 1 , Tazyeen Ahmad 2 1 Associate Professor, Faculty of Engineering and Technology, AMU, Aligarh, UP, India 2 Professor, Faculty of Engineering and Technology, AMU, Aligarh, UP, India, India Abstract - Every organization faces the problem of allocation of resources. The resources include men, machine, material, and capital. Most of these decisions are made subject to constraints. For example, production from a factory is limited due to capacity constraints, and an organization faces working capital constraints and technical constraints. However, if the available resources cannot be expanded, then optimal utilization of existing resources becomes very important task for the organization. Therefore, this paper deals with the idea of optimum utilization of resources to increase the production of toys and hence the profit. In order to achieve this, a technique of linear programming is used. This technique will maximize the profit in production of toys by optimum use of resources. This paper also discusses four important conditions related to productions and their results are tabulated in their respective tables. Firstly the condition of nil production is discussed after that second, third and fourth condition shows the allocation of resources in such a way that continuous increase in profit is achieved. After detailed analysis summary of mathematical results obtained are also tabulated. Keywords: Production, Profit, Machines, Equations 1. INTRODUCTION Linear programming is one of the most versatile, popular and widely used quantitative techniques. A linear programming model offers an efficient method for determining an optimal decision (or an optimal strategy or an optimal plan) chosen from a large number of possible decisions. The optimal decision is one that meets a specified objective or management, subject to various constraints and restrictions [1]. 2. PROBLEM STATEMENT Generally production from companies is limited because of many constraints such as capacity, working capital and technical reasons. 3. METHODOLOGY In order to solve the problem of limited production of electronic toys in any company it is mandatory that resources should be allocated in such a way that maximum production is obtained. This can easily be done by using linear programming. For this work mathematical approach is applied. It is assumed here that there are three machines. The three machines viz. M1, M2 and M3 should be adjusted in such a way that maximum profit is achieved. This is possible only if machines are utilized to its full capacity i.e. when idle time is zero. It is assumed that there are two types of toys DzAdz and DzBdz respectively. Their machine capacity and number of products produced are X1 of type A and X2 of type B and governed by following relation: Machine (1) (2) (3) The first step in this direction is to write inequality in the form of equality equation. This can be done by adding variables S1, S2 and S3 on LHS from the pocket. (4) (5) (6) First of all a trivial solution is tried i.e. X1 and X2 both equal to zero. It will give Profit is always nil when there is no production i.e. i.e. all resources are idle. Now solution is to be developed in such a manner that gives a combination of minimum value of S1, S2, S3 and in turn will maximize the value of objective function Z [2].