Use the graphical method for linear programming to find the optimal solution for the following problem.
Minimize C = 6x + 10y
subject to $2 x + 4 y \geq 12$
$\begin{array} { l }
5 x + 2 y \geq 10 \
and~~~~x \geq 0 , y \geq 0 .
\end{array}$
A) (x, y) = (0, 0)
B) (x, y) = (0, 3)
C) (x, y) = (0, 5)
D) (x, y) = (1, 2.5)
E) (x, y) = (6, 0)

Question

Use the graphical method for linear programming to find the optimal solution for the following problem.
Minimize C = 6x + 10y
subject to $2 x + 4 y \geq 12$
$\begin{array} { l } 
5 x + 2 y \geq 10 \
and~~~~x \geq 0 , y \geq 0 .
\end{array}$
A) (x, y) = (0, 0)
B) (x, y) = (0, 3)
C) (x, y) = (0, 5)
D) (x, y) = (1, 2.5)
E) (x, y) = (6, 0)

Quizplus · Accepted Answer

The graphical method involves plotting the constraints on a graph, identifying the feasible region, and then finding the point(s) in this region that minimize the objective function. The constraints $2x + 4y \geq 12$ and $5x + 2y \geq 10$, along with $x \geq 0$ and $y \geq 0$, define a feasible region. The optimal solution (where the objective function $C = 6x + 10y$ is minimized) is at the point where the objective function's contour line is tangent to the feasible region or at a corner point of the feasible region. Among the given options, (1, 2.5) is the point that lies within the feasible region and results in the minimum value of C when substituted into the objective function, making it the optimal solution.

Use the Graphical Method for Linear Programming to Find the Optimal