In this assignment, you will investigate the use of Linear programming model to solve a real problem.

Example:

To maximize profits, a plastic toy manufacture seeks to optimize their production mix.

They make customized automobile and aircraft toys. A case of planes makes $$25$ in profit, whereas a case of cars makes $$20.$ A device known as a plastic extruder, which runs on plastic resins, is used to make the toys. For every plane case, $20$ pounds of plastic resin are needed, but each car case needs $12$ pounds. Plastic resins can only be produced in quantities of no more than $1800$ pounds each day. Either product can be manufactured in about $15$ cases per hour. The proprietor of the manufacturer currently wants to work only $8$ hours a day.

$1-$ Identify the decision variables?

$2-$ Write the objective function?

$3-$ Identify the constraints?

$4-$ Find the optimal solution and the optimal value using the Graphical Analysis.