# Business Uses of a Linear Programming Model

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Businesses use linear programming methods to determine the best ways to increase profits and decrease operational costs. Linear programming methods enable businesses to identify the solutions they want for their operational problems, define the issues that may alter the desired outcome and figure out an answer that delivers the results they seek. Although the phrase "linear programming" came into use well before the widespread use of computers, software packages are available that replicate the linear programming processes.

## Production Planning

Linear programming methods are often helpful at solving problems related to production. A company that produces multiple types of products can use linear programming methods to calculate how much of each product to produce to maximize its profits. For instance, a custom furniture shop that makes chairs and tables can calculate how many of each item they must sell to maximize their profits by looking at the numbers of each item previously sold and their prices.

## Marketing Mix

A key aspect of marketing strategy is the "marketing mix." The marketing mix determines how much of a company's marketing budget will go toward various advertising and marketing channels. A linear programming simulation can measure which blend of marketing avenues deliver the most qualified leads at the lowest cost. For example, the custom furniture store can use a linear programming method to examine how many leads come from TV commercials, newspaper display ads and online marketing efforts. The solution will also compare the relative prices of each medium to find the most economical mix.

## Product Distribution

Manufacturers and distributors can use linear programming methods to solve distribution problems. These mathematical exercises can help manufacturers determine the most cost-effective way to ship products from the factory to the warehouse. Warehouse managers can also use similar models to calculate the most economical way to transport the products from the warehouse to the retail outlets. These models can also ensure that warehouses maintain an optimal amount of each product in stock as demand fluctuates.

## Personnel Assignments

Human resources planners can use linear programming methods to determine when to hire more workers, which skill sets the company needs and how much they can offer in compensation. These methods can also be used to anticipate times of increased demand for available workers. For example, a department store can use linear programming methods to calculate how many new hires they will make for the busy holiday shopping season, as well as which departments will see higher traffic and require more staff.

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