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

question 168

Multiple Choice

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

Z = 4x + 16y

Constraints:

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

• A)Minimum at \(\left( 0 , \frac { 19 } { 6 } \right)\) : \(\frac { 152 } { 3 }\)
• B)Minimum at \(\left( \frac { 22 } { 3 } , 0 \right)\) : \(\frac { 88 } { 3 }\)
• C)Minimum at (0, 0): 0
• D)Minimum at \(\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)\) : 80
• E)No minimum

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Definitions:

Moral

Pertaining to the principles of right and wrong behavior and the goodness or badness of human character.

Partnership Termination

The process of dissolving a business partnership, involving the liquidation of assets, settlement of debts, and distribution of remaining assets among partners.

Liquidation

The process of converting assets into cash, often in the context of dissolving a company or settling debts.

Dissolution

The process of formally ending or disbanding something, such as a business, marriage, or legal contract, often through legal means.