Constraints linear programming graphical

LINEAR PROGRAMMING GRAPHICAL SOLUTION. Figure 11-9 is the graphical representation of this problem. Line OE represents the overall constraint placed on the problem by Eqs. (58), (59), and (60). The parallel dashed lines represent possible conditions of cost. The goal of the program is to minimize cost (that is, C) while still remaining within the constraints of the problem. The minimum value of C that still meets the constraints occurs for the line OD, and the optimum must be at point 0. Thus, the recommended blend is no water, 37.5 gal of A, 62.5 gal of B, and a total cost C of 27.63 for 100 gal of blend. 

This graphical technique is adequate for the two variables investigated in this problem. This problem can also be solved using optimization techniques such as linear programming, a technique that can handle numerous constraints and variables... 

In Equation (3.1), Z is the objective fimction, while the variables Xj and X2 are called design variables, and represent the number of 16-ft -capacity tanks and the number of 24-6 -capacity tanks, respectively. The limitations imposed by the inequalities in Equations (3.2)— (3.5) are referred to as a set of constraints. Althou there are specific techniques that deal with solving linear programming problems (the objective fimction and constraints are linear), we will solve this problem graphically to illustrate some additional concepts. 

Figure 10.3 Graphical representation of linear programming with two and three roof constraints.

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