Minimize w= y1+y2+4y3
subject to y1+2y2+3y3>=115
2y1+y2+y3<=200
y1+ y3>=50
with y1 >=0 y2>=0 y3>=0
Graphics is too hard for me to use with three variables. Here is a good outline how to use Excel (and compariable) spreadsheets.
http://www.cob.sjsu.edu/anaya_j/LinPro.htm
THe sign change in row three is not a sign change it is a misprint it really is and >= sign.
To minimize the given objective function w = y1 + y2 + 4y3 subject to the given constraints, we can use linear programming.
Linear programming is a mathematical optimization technique used to find the best possible outcome given a set of linear constraints and an objective function.
To solve this problem, we can follow these steps:
Step 1: Define the decision variables:
Let y1, y2, and y3 represent the decision variables.
Step 2: Formulate the objective function:
The objective function is to minimize w = y1 + y2 + 4y3.
Step 3: Formulate the constraints:
The given constraints are:
1) y1 + 2y2 + 3y3 >= 115
2) 2y1 + y2 + y3 <= 200
3) y1 + y3 >= 50
Additionally, we have the non-negativity constraints: y1 >= 0, y2 >= 0, y3 >= 0.
Step 4: Combine the objective function and constraints:
Combine the objective function and constraints to form a feasible region.
Step 5: Solve the linear programming problem:
Solve the linear programming problem using optimization techniques such as the Simplex method or graphical method.
By solving the linear programming problem, you will obtain the optimal values of y1, y2, and y3 that minimize the objective function w(subject to the given constraints). The optimal solution will satisfy the constraints and give you the minimum value of w.