Consider the following linear programming model. Let X and Y be the two decision

variables. The objective of the model is maximization, and the objective function is $2$X $+$ Y In addition to

X $>=0$ and Y $>=0$ there are two functional constraints: x $+$ y $<=5$ and $3$X $+2$Y $>=10$

The whole model is given below: subject to X $+$ Y $<=5$

Maximize $2$X $+$ Y

$3$X $+2$Y $>=10$

x $>0$ Y $>=0$

c$)$ Mathematically formulate the dual of the linear programming model given above $($the primal model$).$ To do so$,$ clearly define the dual variables and which constraints of the primal model they correspond to$.$

d$)$ Given the optimal primal solution from your solution in part a$,$ determine optimum

$?$