1 linear programming model
A, linear programming topic:
Example 1: production planning problem
Suppose a factory plans to produce two kinds of products, A and B. The main materials in stock are A 3600kg, B 2000kg and C 3000kg. Each A product needs 9 kg of materials of Class A, 4 kg of materials of Class B and 3 kg of materials of Class C. Each B product needs 4 kg of materials of Class A, 5 kg of materials of Class B, and materials of Class C10 kg ... 70 yuan, a unit product profit. Ask how to arrange production in order to maximize the profit of this factory.
Establish a mathematical model:
Let x 1 and x2 be the product quantities produced by Party A and Party B respectively. F is the total profit made by this factory.
Maximum f=70x 1+ 120x2.
s.t 9x 1+4x2≤3600
4x 1+5x2≤2000
3x 1+ 10x2≤3000
x 1，x2≥0
It boils down to a programming problem: both the objective function and the constraint conditions are linear functions of the variable X.
Shape: (1) minimum f T X
Standard time A X≤b
Aeq X =beq
lb≤X≤ub
Where x is an n-dimensional unknown vector, f T=[f 1, f2, …fn] is the objective function coefficient vector, the constraint coefficient matrix A is less than or equal to m×n matrix, b is the right m-dimensional column vector, Aeq is the equality constraint coefficient matrix, and beq is the right constant sequence vector constrained by equality. Lb and UB are n-dimensional constant vectors with upper and lower bounds of independent variables.
2. The function of finding the optimal solution of linear programming problem:
Call format: x=linprog(f, a, b)
x=linprog(f，A，b，Aeq，beq)
x=linprog(f，A，b，Aeq，beq，lb，ub)
x=linprog(f，A，b，Aeq，beq，lb，ub，x0)
x=linprog(f，A，b，Aeq，beq，lb，ub，x0，options)
[x，fval]=linprog(…)
[x，fval，exitflag]=linprog(…)
[x，fval，exitflag，output]=linprog(…)
[x，fval，exitflag，output，lambda]=linprog(…)
Description: x=linprog(f, a, b) The return value x is the optimal solution vector.