What Does Linear Mean In Math latest 2023

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Understanding The Concept Of Linear Programming

Linear programming is an operations research technique that emerged in the early 1950s. Having various practical applications, the technique has immensely benefited various organizations in their production and other operations. Professor GB Dantzig is one of the pioneers in the formulation of the linear programming procedure.

This technique can be applied in a variety of situations: long-term planning, production planning, warehousing decisions, physical distribution decisions, marketing and product mixing decisions, fluid mixing problems, oil field exploration, purchasing decisions, quality control decisions, material usage decisions, etc.

The basic problem solved by linear programming is that of optimizing profit or total costs or some other utility function. It takes into consideration limitations or constraints on the availability or use of different resources such as labor, machinery, materials, time and money as well as other limitations and constraints such as those existing in the market (for example, a limited number of units of a product might be sold) or quality specifications such as the maximum or minimum limits of the performance characteristics of a particular product, etc. In short, linear programming deals with optimizing a desired goal in a situation where there are various constraints. Most management problems are optimal decision-making problems performed under various limitations. This is why linear programming deservedly attracts the attention of practicing executives.

We can illustrate what linear programming means through a simple example. Suppose a firm produces two products X and Y, both of which require a particular raw material and a particular machine. Product X requires 4 machine hours and 3 kg of raw material per product unit, and product Y requires 2 machine hours and 6 kg of raw material per product unit. Suppose the availability of machine hours and raw material is limited. The raw material is available at the maximum of only 240 kg per month and the machine hours are available at the maximum of only 200 machine hours per month. Each of the products X and Y contributes to the profit margin of $7 and $9 respectively per product unit. How many units of products X and Y should the company produce each month?

To solve the above problem, you need to clearly understand the concept of linear programming and apply it in the right way. If you face any problems while learning this concept, you can take the help of private tutors. Finding the right private tutor for a particular subject, location and time period is possible via the internet. You just need to take time out of your busy schedule to find online tutoring services.

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