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

question 7

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