Buffro $($Pty$)$ Ltd manufactures two types of cooler bags, the Cool and the Ice. information about the bags is given in the following table.

$\backslash$table$[[,$Cool,Ice$],[$Selling price per unit,R$200,$R$210],[$Variable cost per unit,$88,80],[$Material $($R$2\mathrm{.}50$; $8$kg and $10$ kg respectively$),20,25],[$Labour $($R$4\mathrm{.}00$; $10$ hours and $5$ hours respectively$),40,20],[\backslash$table$[[$Variable overhead $($R$7\mathrm{.}00$; $4$ hours and $5$ hours$],[$respectively$)]],28,35],[\backslash$table$[[$Contribution per unit$]],112,130],[$Maximum demand,$350$ units,$350$ units$]]$

Limitations of resources are as follows:

Material

$31000$ kg

Labour

$20000$ labour hours

Variable overheads

$17500$ machine hours

The maximum demand is $1000$ units of the Cool and $3000$ units of the Ice.

Required:

Prepare a linear programming solution for the limited resources of Buffro $($Pey$)$

Ltd using:

The graphical method with simultaneous equations

The simplex method.