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

question 261

Multiple Choice

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

Z = 5x + y

Constraints:

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

• A)Maximum at (0, 5): 5
• B)Maximum at \(\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)\) : \(\frac { 239 } { 6 }\)
• C)Maximum at (0, 0): 0
• D)No maximum
• E)Maximum at \(\left( \frac { 21 } { 2 } , 0 \right)\) : \(\frac { 105 } { 2 }\)

---

Definitions:

Stomach Ulcers

Sores that develop on the lining of the stomach, upper small intestine, or esophagus, often resulting from Helicobacter pylori infection or the use of NSAIDs.

Helicobacter Pylori

A type of bacteria that infects the stomach lining and is associated with ulcers and some forms of stomach cancer.

Escherichia Coli

A type of bacteria commonly found in the intestines of humans and animals, some strains of which can cause food poisoning.

Basal Metabolic Rate

Rate at which the body uses energy when at rest.