QUESTION $6(25$ marks; $45$ minutes$)$

$103$ Field Workshop, a technical service providing mechanical services to all SANDF bases in the Westem Cape, has a division that makes the brown paint for the army fleet, and a white paint for the navy and air force fleet.

Information about the paints is given in the table below:

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline & Brown & White $\backslash \backslash$

$\backslash$hline Selling price per litre & R$200$ & R$210\backslash \backslash$

$\backslash$hline Variable cost per litre: & & $\backslash \backslash$

$\backslash$hline Material $($R$2\mathrm{.}50$; $8$ litres $\backslash$& $10$ litres respectively$)$ & R$20$ & R$25\backslash \backslash$

$\backslash$hline Labour $($R$4\mathrm{.}00$; $10$ hours $85$ hours respectively$)$ & R$40$ & R$20\backslash \backslash$

$\backslash$hline Variable overhead $($R$7\mathrm{.}00$; $4$ hours and $5$ hours respectively$)$ & R$28$ & R$35\backslash \backslash$

$\backslash$hline Minimum demand $($litres$)$ & $350$ & $350\backslash \backslash$

$\backslash$hline Limitations of resources are as follows: & & $\backslash \backslash$

$\backslash$hline Material $\backslash (\backslash$quad $31000\backslash$mathrm$\{$~kg$\}\backslash )$ & & $\backslash \backslash$

$\backslash$hline Labour $20000$ hours & & $\backslash \backslash$

$\backslash$hline Variable overhead $17500$ machine hours & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Required:

$6\mathrm{.}1$ Prepare a linear programming solution for the limited resources of $103$ Field Workshop using the graphical method with simultaneous equations to support your answer. $(25)$

$($Her$\text{'}$t$)$

Sown $\backslash (=$x $\backslash )$