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

Question 1

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) $Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: z = 7 x + \frac { 1 } { 4 } y Constraints: \begin{aligned} x & \geq 0 \\ y & \geq 0 \\ \frac { 1 } { 2 } x + y & \leq 8 \\ x + \frac { 1 } { 2 } y & \geq 4 \end{aligned} A) Minimum at (8, 0) : 3.00 B) No minimum C) Minimum at (4, 0) : 28.00 D) Minimum at (16, 0) : 112.00 E) Minimum at (0, 8) : 2.00$ Minimum at (8, 0) : 3.00
B) $Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: z = 7 x + \frac { 1 } { 4 } y Constraints: \begin{aligned} x & \geq 0 \\ y & \geq 0 \\ \frac { 1 } { 2 } x + y & \leq 8 \\ x + \frac { 1 } { 2 } y & \geq 4 \end{aligned} A) Minimum at (8, 0) : 3.00 B) No minimum C) Minimum at (4, 0) : 28.00 D) Minimum at (16, 0) : 112.00 E) Minimum at (0, 8) : 2.00$ No minimum
C) $Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: z = 7 x + \frac { 1 } { 4 } y Constraints: \begin{aligned} x & \geq 0 \\ y & \geq 0 \\ \frac { 1 } { 2 } x + y & \leq 8 \\ x + \frac { 1 } { 2 } y & \geq 4 \end{aligned} A) Minimum at (8, 0) : 3.00 B) No minimum C) Minimum at (4, 0) : 28.00 D) Minimum at (16, 0) : 112.00 E) Minimum at (0, 8) : 2.00$ Minimum at (4, 0) : 28.00
D) $Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: z = 7 x + \frac { 1 } { 4 } y Constraints: \begin{aligned} x & \geq 0 \\ y & \geq 0 \\ \frac { 1 } { 2 } x + y & \leq 8 \\ x + \frac { 1 } { 2 } y & \geq 4 \end{aligned} A) Minimum at (8, 0) : 3.00 B) No minimum C) Minimum at (4, 0) : 28.00 D) Minimum at (16, 0) : 112.00 E) Minimum at (0, 8) : 2.00$ Minimum at (16, 0) : 112.00
E) $Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: z = 7 x + \frac { 1 } { 4 } y Constraints: \begin{aligned} x & \geq 0 \\ y & \geq 0 \\ \frac { 1 } { 2 } x + y & \leq 8 \\ x + \frac { 1 } { 2 } y & \geq 4 \end{aligned} A) Minimum at (8, 0) : 3.00 B) No minimum C) Minimum at (4, 0) : 28.00 D) Minimum at (16, 0) : 112.00 E) Minimum at (0, 8) : 2.00$ Minimum at (0, 8) : 2.00

Correct Answer:

Verified

Select the Region Determined by the Constraints z=7x+14yz = 7 x + \frac { 1 } { 4 } yz=7x+41​y

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