paints must not exceed $\mathrm{.}5.$

$2-2.$ Determine the best feasible solution among the following $($feasible and infeasible$)$ solutions of the Reddy Mikks model:

$($a$)x_1=1,x_2=2.$

$($b$)x_1=3,x_2=1.$

$($c$)x_1=3,x_2=1\mathrm{.}5.$

$($d$)x_1=2,x_2=1.$

$($e$)x_1=2,x_2=-1.$

$2-3.$ For the feasible solution $x_1=1,x_2=2$ of the Reddy Mikks model, determine the unused amounts of raw materials $M1$ and $M2.$

$2-4.$ Suppose that Reddy Mikks sells its exterior paint to a single wholesaler at a quantity discount. The profit per ton is $$5000$ if the contractor buys no more than $5$ tons daily and $$4300$ otherwise. Express the objective function mathematically. Is the resulting function linear?

$2-5.$ Determine the feasible space for each of the following independent constraints, given that $x_1,x_2=0.$

$($a$)-3x_1+x_{2}6.$

$($b$)x_1-2x_{2}5.$

$($c$)2x_1-3x_{2}12$

$($d$)x_1-x_{2}0.$