$(5-2)Do$ Exercise $5-1$ for the $LP$

$3{}_1+5{}_{2}15$

$5{}_1+3{}_{2}15$

${}_1,{}_{2}0$

$(a)$ sketch the feasible space $ina2-$dimensional plot

$(b)$ Determine geo met rically whether cach $of$ the following Solutions are infeasible, boundry,

extreme, and $or$ interior${}^{(1)}=(0,0),{}^{(2)}=(1,1),{}^{(3)}=(2,0),$

${}^{(4)}=(3,3),{}^{(5)}=(5,0)$

$(c)$ For those points $of$ part $(b)$ that are feasible, demonstrate algebraically whether

they are boundary $or$ interior.

$(d)$ Determine for each $of$ the paints $in$ part $(b)$ whether a Suitable $(non$ Constant$)$ objective

function could make the paint optimal $or$ uniquely optimal. Explain

$(e)$ Determine which $of$ the points Correspond $to$ basic Solution, and when they $do,$ identify

the defining active constraints.