Find the Maximum Value of the Objective Function and Where $\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)$

question 1

Multiple Choice

Find the maximum value of the objective function and where it occurs,subject to the constraints: ?
Objective function:
?
Z = x + 9y
?
Constraints:
?
X ? 0
Y ? 0
X + 4y ? 20
X + y ? 18
?2x + 2y ? 21
?

• A)Maximum at (0,5): 45
• B)Maximum at \(\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)\) : \(\frac { 215 } { 6 }\)
• C)No maximum
• D)Maximum at (0,0): 0
• E)Maximum at \(\left( \frac { 21 } { 2 } , 0 \right)\) : \(\frac { 21 } { 2 }\)

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Definitions:

Marginal Returns

The additional output or benefit received from producing one more unit of a good or service.

Marginal Cost

The cost added by producing one additional unit of a product or service, a crucial concept for making economic decisions.

Average Total Cost

The total cost divided by the quantity produced, indicative of the cost per unit of output.

Average Fixed Cost

Fixed cost divided by output.