Question

Solve the following optimization problem. Minimize

J = x + 3y + 2z

subject to the constraints

Answer 1

MuPAD can be used to solve both symbolic and numeric types of calculations. MuPAD can be run by entering mupadwelcome in the command window.

 

To solve optimization problems using MuPAD, the constraint equations and the optimization problem are defined and the solution is obtained using the linopt::minimize function.

 

The program can be defined as:

 

Define the constraints as:

eq1:=3*x+3*y-3*z<=20;eq2:=6*x-4*y-3*z=20;eq3:=7*x+4*y+11*z<=50

 

Define the optimization problem as:

J:=[{eq1, eq2, eq3}, x+3*y+2*z]

 

Solve the optimization problem:

linopt::minimize(J)

The result obtained is:

 

Define the constraints as:

 

Define the optimization problem as:

 

Solve the optimization problem:

 

Thus, the given optimization problem has been solved and the solution is unbounded.

Thus, the given optimization problem has been solved and the solution is unbounded.