Question #88148

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

Expert's answer

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.

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