Select the Region Determined by the Constraints $$z = 7 x + \frac { 1 } { 8 } y$$

question 14

Multiple Choice

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible) and where it occurs,subject to the indicated constraints. ?
Objective function:? $$z = 7 x + \frac { 1 } { 8 } y$$ ?
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) Maximum at (4,0): 28.00
• B) Maximum at (8,0): 2.00
• C) Maximum at (16,0): 112.00
• D) No maximum
• E) Maximum at (0,8): 1.00

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Definitions:

Fruit and Vegetable Consumption

The intake of fruits and vegetables as part of one's diet.

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The process by which cells convert glucose into energy, involving pathways like glycolysis and the citric acid cycle.

Metabolic Syndrome

A cluster of conditions—increased blood pressure, high blood sugar, excess body fat around the waist, and abnormal cholesterol levels—that occur together, increasing your risk of heart disease, stroke, and diabetes.

Type 1 Diabetes

An autoimmune condition where the pancreas produces little or no insulin, requiring daily insulin administration for management.