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

question 22

Multiple Choice

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

Z = 12x + 24y

Constraints:

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

• A)Maximum at (0, 5): 120
• B)Maximum at \(\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)\) : 164
• C)No maximum
• D)Maximum at \(\left( \frac { 21 } { 2 } , 0 \right)\) : 126
• E)Maximum at (0, 0): 0

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Definitions:

General Equilibrium

An economic state where supply and demand are balanced across all markets in the economy simultaneously.

Continuous Demand

Demand for a good or service that can be quantified at every level of production or price, without any gaps.

First Theorem of Welfare Economics

A principle stating that under certain conditions, a market in equilibrium will allocate resources efficiently in a way that maximizes total social welfare.

Competitive Equilibrium

A market state where supply equals demand, leaving no incentive for price changes as long as external conditions remain constant.