Answer to Question #88148 in Operations Research for Penuell

Question

Maximize z=3a+b+2c
Subject to: a + b+ 3c <=30, a>=0, b>=0, c>=0.

Answer 1

Maximize z=3a+b+2c

Subject to: a + b+ 3c <=30, a>=0, b>=0, c>=0.

Solution: Formally, we have a linear programming problem. It includes only one constraint. Thus, there will be only one basis variable in the solution. The variable a has the highest ratio of the coefficient in the objective function to the coefficient in the constraint: 3/1=max{3/1;1/1;2/3}. Therefore, we have to assign the variable a the maximum of the possible values: a=30. So, b=c=0,

z _max=z(30;0;0)=90.

Answer: a=30, b=c=0, z_max=90.