question 16 find the maximum of the objective function ( c = 5x + 9y ) subject to the feasibility region…

Explanation:

Step1: Identify vertices of feasible region

The vertices from the graph are $(1,1)$, $(8,1)$, $(5,5)$, $(1,8)$.

Step2: Calculate $C$ at $(1,1)$

Substitute $x=1,y=1$ into $C=5x+9y$: $C=5(1)+9(1)=5+9=14$

Step3: Calculate $C$ at $(8,1)$

Substitute $x=8,y=1$ into $C=5x+9y$: $C=5(8)+9(1)=40+9=49$

Step4: Calculate $C$ at $(5,5)$

Substitute $x=5,y=5$ into $C=5x+9y$: $C=5(5)+9(5)=25+45=70$

Step5: Calculate $C$ at $(1,8)$

Substitute $x=1,y=8$ into $C=5x+9y$: $C=5(1)+9(8)=5+72=77$

Step6: Compare $C$ values

$14 < 49 < 70 < 77$

Answer:

The maximum value of $C$ is 77, which occurs at the point $(1,8)$.