The idea of solving the problem is: firstly, the constraint conditions are illustrated, and the solution set (row domain) satisfying the constraint conditions is obtained, and then the optimal solution is found from the feasible domain according to the requirements of the objective function.
Chinese Name: Graphical Method of Linear Programming mbth: Linear Programming Discipline: Operational Research Essence: Finding the Optimal Solution through Geometric Drawing Advantages: Intuitive, Image-related nouns: Basic concepts and general steps of linear programming model, for example, the feasible solution of basic concepts refers to a group of decision variables that satisfy constraints as the feasible solution of linear programming problems. Feasible Solution Set/Feasible Solution Domain All feasible solutions that meet the constraint conditions are called feasible solution sets. On the plane, the point set of all feasible solutions is called feasible solution domain. The optimal solution is in the feasible solution set, and the feasible solution that makes the objective function reach the optimal value is called the optimal solution. General step 1: Establish a mathematical model. 2. Draw the graph of constraint inequality, so that the feasible solution domain corresponds to the feasible solution set. 3. Draw the target function diagram. 4. Judge the form of the solution and draw a conclusion. For example (1). Constraints: (2) Draw feasible solution domain: (3) Draw objective function diagram: Make the objective function value zero to get slope, and make a straight line through the origin according to the slope. (If the feasible solution domain is in the first quadrant, the slope of the objective function isoline is negative) If the given problem is to seek the maximum value, the objective function isoline is moved in parallel to the point where it finally intersects with the feasible solution domain, which is the optimal solution of the problem; If the given problem is to find the minimum value, then the isoline of the objective function moves in parallel to the point where it intersects the feasible solution domain for the first time, which is the optimal solution of the problem. (4) Judge the form of the solution and draw a conclusion. This problem has a unique optimal solution. Solution: the optimal solution is the final intersection point determined by two straight lines; Solve the equations formed by the equations corresponding to these two lines, and get the exact optimal solution of the problem; Substitute the optimal solution into the objective function to get the optimal value. Substituting the optimal solution into the objective function to obtain the optimal value: