Use the Given Feasible Region Determined by the Constraint Inequalities $x$

question 112

Multiple Choice

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
-Find the values of $x$ and $y$ that give the minimum possible value of $f = 6 x + 8 y$ subject to the following constraint $\left\{ \begin{array} { l } 2 x + 4 y \geq 12 \\ 2 x + y \geq 8 \\ x \geq 0 , y \geq 0 \end{array} \right.$

• A) \(x = 0 , y = 3\)
• B) \(x = 0 , y = 0\)
• C) \(x = \frac { 10 } { 3 } , y = \frac { 4 } { 3 }\)
• D) \(x = 6 , y = 0\)

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Definitions:

Set Point

The desired or target value for a controlled variable in a control system, against which actual values are compared to determine the need for corrective action.

Proportioning Action

A control method where the output is adjusted in proportion to the difference between the actual value and a setpoint.

Proportional Band

A control parameter in PID controllers that determines the range of proportional action surrounding a setpoint for maintaining system stability.