Linear Prgramming

<aside> 💡 Optimization Task with Linear Constraints and Object functions

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해결 방법

1. identify Variables, Linear Equations, Linear Inequalities, Linear Objective functions and Fomulate problem in LP
2. find real values to max/min objective function
   1. Profit Maximization

Profit Maximization

ex. chocolate products

• Variable
  • x1: amount of A to produce per day
  • x2: amount of B to produce per day
• Constraints
  • Range of Var
    • x1, x2 ≥ 0
  • Demand: 200, 300
    • x1 ≤ 200
    • x2 ≤ 300
  • Capacity: ≤ 400
    • x1+x2 ≤ 400
• Objective Function
  • maximum profit : optimal production
    • max x1+6x2

모든 constraint를 만족하는 구간을 Feasible Region이라고 한다.

objective function의 feasible region 내에서 최대를 구하자

Simplex Method

Optimum is achieved at A vertex of the feasible region

except: