Select the Region Determined by the Constraints $z = 7 x + \frac { 1 } { 4 } y$

question 159

Multiple Choice

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints.
Objective function:
$z = 7 x + \frac { 1 } { 4 } y$
Constraints: $\begin{aligned}x & \geq 0 \\y & \geq 0 \\\frac { 1 } { 2 } x + y & \leq 8 \\x + \frac { 1 } { 2 } y & \geq 4\end{aligned}$

• A) Minimum at (8, 0): 3.00
• B) No minimum
• C) Minimum at (4, 0): 28.00
• D) Minimum at (16, 0): 112.00
• E) Minimum at (0, 8): 2.00

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Definitions:

Right Side of the Brain

The hemisphere of the brain that is often associated with creative thinking, intuition, and artistic abilities, contrasting with the left side's analytical and logical functions.

Hemispheric Specialization

The distinction in cognitive functions between the left and right hemispheres of the brain, where each hemisphere is specialized for certain tasks.

Glial Cells

Non-neuronal cells in the central nervous system that support, protect, and nourish neurons, playing a key role in maintaining homeostasis.

Neurons

Specialized cells within the nervous system that transmit information to other nerve cells, muscle, or gland cells.