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

---

Definitions:

Detoxify

The process of removing toxic substances or qualities, often referring to the liver's role in cleaning blood or to treatments for drug dependence.

Interstitial Fluid

Interstitial fluid is the fluid that surrounds cells within tissues, facilitating the exchange of nutrients, waste products, and other molecules between blood and cells.

Cardiac Muscle Fiber

Specialized muscle fibers found in the heart, characterized by their striations, intercalated discs, and ability to contract rhythmically.

Chloride Ions

Negatively charged ions (Cl-) that are an essential component of bodily fluids and play key roles in fluid balance and transmission of nerve impulses.