Consider the following linear programming problem:

Minimize : $C=0\mathrm{.}30x+0\mathrm{.}40y$

Subject $to$ :$,210x+150y2115$

$240x+380y3460$

$x,y0$

When graphed and shaded, the following corner points are discovered:

$(0,14\mathrm{.}1)$

$(6\mathrm{.}5,5)$

$(\frac{173}{12},0)$

What is the solution to the problem?

$C$ is minimized at $3\mathrm{.}95$ when $x=6\mathrm{.}5$ and $y=5$

$C$ is minimized at $4\mathrm{.}325$ when $x=\frac{173}{12}$ and $y=0$

$C$ is minimized at $5\mathrm{.}64$ when $x=0$ and $y=14\mathrm{.}1$

$C$ is maximized at $5\mathrm{.}64$ when $x=0$ and $y=14\mathrm{.}1$