PROBLEM $1(50$ points$)$

The Stratton Company produces two basic types of plastic PVC pipe $($Type $1$ and Type $2).$ Three resources $($operations$)$ are crucial to the output of pipes; extrusion hours, packaging hours and special additive to the plastic raw material. The following data represent resources availability for next week on the Production Department. All data are expressed in units of $100$ feet of pipe $($i$.$e$.1$ unit $=100ft.$ of pipe$)$

$\backslash$table$[[$PRODUCT$,],[$Resource$,$Type $1,$Type $2,$Resource Availability$],[$Extrusion$,4$ hr$,6$ hr$,48$ hr$],[$Packaging$,2$ hr$,2$ hr$,18$ hr$],[$Additive mix,$2$ b$,1$ hb$,16$ lb$]]$

Profit of each Type $1$ pipe sold is $$34.$ Profit of each Type $2$ pipe sold is $$49.$

For the situation presented above:

a$)$ Develop complete Linear Programming Formulation.

b$)$ Solve problem using graphical method.

c$)$ How many units $($and feet$)$ of each type of pipe should be produced in order to maximize profit assuming that everything produced can be sold. What would be that profit?

Note: Present graph and all calculations