Solve the following linear program: Identify the optimal solution.

Minimize $C=3x+4y$

Subject to:

$3x-4y12,A$

$x+2y4,B$

$x1C$

$x,y0,$

$(1,1\mathrm{.}5)$

$(1,2\mathrm{.}5)$

$(4,0)$

$(2\mathrm{.}5,2\mathrm{.}5)$