mathematical approach to the problem of allocating limited resources among competing activities in an optimal manner. Specifically, it is a technique used to maximize revenue, Contribution Margin (CM) , or profit function or to minimize a cost function, subject to constraints. Linear programming consists of two important ingredients: (1) objective function and (2) constraints, both of which are linear. In formulating the LP problem, the first step is to define the decision variables that one is trying to solve. The next step is to formulate the objective function and constraints in terms of these decision variables. For example, assume a firm produces two products, A and B. Both products require time in two processing departments, assembly and finishing. Data on the two products are as follows:
Products
A B Available
Assembly (hours) 2 4 100
Finishing (hours) 3 2 90
CM/unit $25 $40
The firm wants to find the most profitable mix of these products. First, define the decision variables as follows:
A = the number of units of product A to be produced
B = the number of units of product B to be produced
Then, express the objective function, which is to maximize total contribution margin (TCM), as:
TCM = $25A + $40B
Formulate the constraints as inequalities:
2A + 4B < 100
3A + 2B < 90
and do not forget to add the non-negative constraints:
A > 0, B > 0
Source: http://www.allbusiness.com/glossaries/linear-programming-lp/4942501-1.html#ixzz1mJdRngMo
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