$2)$ Solve the following linear program:

Max $3$x $+2$y

subject to: x $<=6$

x $+$ y $<=8$

$2$x $+$ y $>=8$

$2$x $+3$y $>=12$

$3)$ Expedition Outfitters manufactures a variety of specialty clothing for hiking, skiing and mountain

climbing. The management decided to begin production on two key new parkas design for use in

extremely cold weather: the Mountain Parka and the Rocky Parka. The manufacturing plant has $40$

hours of cutting time and $52$ hours of sewing time available for producing these two parkas. Each

Mountain Parka requires $30$ minutes of cutting time and $45$ minutes of sewing time, and each Rocky

Parka requires $45$ minutes of cutting time and $15$ minutes of sewing time. The retail prices through the

firm$$s mail order catalog are $$105$ for the Mountain Parka and $$85$ for Rocky Parka. Management also

requires at least $20$ Mountain Parkas manufactured. Assuming that Expedition Outfitters can sell as

many coats of each type as it can produce, how many units of each model should it manufacture to

maximize the total profit contribution? Find the optimal solution