Find the Maximum Value of the Objective Function and Where $\ge$

question 179

Multiple Choice

Find the maximum value of the objective function and where it occurs, subject to the constraints:
Objective function:

Z = 8x + 9y

Constraints:

X $\ge$ 0
Y $\ge$ 0
X + 4y $\le$ 20
X + y $\le$ 18
2x + 2y $\le$ 21

• A)Maximum at \(\left( \frac { 22 } { 3 } , 0 \right)\) : \(\frac { 176 } { 3 }\)
• B)Maximum at (0, 0): 0
• C)Maximum at \(\left( 0 , \frac { 19 } { 6 } \right)\) : \(\frac { 57 } { 2 }\)
• D)Maximum at \(\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)\) : \(\frac { 523 } { 6 }\)
• E)No maximum