NOTE: Please use graph paper attached for solving the problem$($s$).$

PROBLEM $1$: GRAPHICAL SOLUTION $(10$ points$)$

a$)(5$ points$)$ Consider the following LP of a version of Reddy Mikks problem:

Maximize $z=3x_1+4x_2$

Subject to

$x_1+2x_{2}6$

$2x_1+x_{2}9$

$-x_1+x_{2}2$

$x_{2}2\mathrm{.}5$

$x_1,x_{2}0$

Use Graphical Solution Method to find all the corner$-$point solutions and determine which corner$-$point is

the optimum solution?

b$)(5$ points$)$ Add the following new constraints to the Reddy Mikks Problem, and change the objective

to minimization. Solve the problem using Graphical Solution Method.

$2x_1+3x_{2}6$

$2x_1+2x_{2}5$

PROBLEM $2$: FORMULATION $(20$ points$)$

The Windsor Glass Company is planning to launch two new products. Product $1$ is an $8-$foot glass door

with aluminum framing and Product $2$ a $46$ foot double$-$hung wood$-$framed window.

Aluminum frames are made in Plant $1,$ wood frames are made in Plant $2,$ and Plant $3$ produces

the glass and assembles the products.

Product $1$ requires some of the production capacity in Plants $1$ and $3,$ but none in Plant $2.$

Product $2$ needs only Plants $2$ and $3.$ The marketing division has concluded that the company

could sell as much of either product as could be processed by these plants. The management of

the company wants to determine what mixture of both products would be the most profitable.

The following table provides the information available.

a$)$ Formulate the problem as LP$.(10$ points$)$

b$)$ Solve the problem using Graphical Solution method. $(10$ points$)$