math 540

 

“Linear Programming Approach” Please respond to the following:

 

•Does the linear programming approach apply the same way in different applications? Explain why or why not using examples.

 

Linear Programming is a mathematical technique for choosing the best alternative form of a set of feasible alternatives. In situations where the objectives function as well as the restrictions or constraints can be expressed as linear mathematical functions. For example

 

 THE DIET PROBLEM:

 

 To find the cheapest combinations of foods that will satisfy all your nutritional requirements.

 

 Example:  Suppose the only foods available in your local store are potatoes and steak. The decision about how much of each food to buy is also made entirely on dietary and economic considerations. We have the nutritional and cost information in the following table: Per unit of potatoes Units of carbohydrates, Units of vitamins, Units of proteins, Unit cost per unit of steak Minimum requirements

 

 The problem is to find a diet (a choice of the numbers of units of the two foods) that meets all minimum nutritional requirements at minimal cost.

 

 a. Formulate the problem in terms of linear inequalities and an objective function.

 

 b. Solve the problem geometrically.

 

 We begin by setting the constraints for the problem. The first constraint represents the minimum requirement for carbohydrates, which are 8 units per some unknown amount of time. 3 units can be consumed per unit of potatoes and 1 unit can be consumed per unit of steak. The second constraint represents the minimum requirement for vitamins, which are 19 units. 4 units can be consumed per unit of potatoes and 3 units can be consumed per unit of steak. The third constraint represents the minimum requirement for proteins, which are 7 units. 1 unit can be consumed per unit of potatoes and 3 units can be consumed per unit of steak. The fourth and fifth constraints represent the fact that all feasible solutions must be nonnegative because we can’t buy negative quantities.