Question $5(15$ marks; $27$ minutes$)$

Denel Munitions produces three products, A$110,$ B$382$ and C$657.$ Unit data for the three products is as follows:

$\backslash$table$[[,$Product Information$],[$A$110,$B$382,$C$657],[$Selling price,R$840,$R$560,$R$700],[$Variable costs:,,,$],[$Direct materials $($Sulphide$),$R$240,$R$150,$R$90],[,$ Labour and other costs,R$280,$R$270,$R$400],[$Quantity of Sulphide per unit,$8$ kg$,5$ kg$,3$ kg$]]$

All three products use the same direct material, Sulphide. The demand for the products far exceeds the direct materials available for the current production. Sulphide costs R$30$ per kilogram and a maximum of $5000$ kilograms is available each month. Denel Munitions must produce a maximum of $400$ units of each product, and these demand maximums include a contract for the delivery of $50$ units of each product to an important client.

Required: $$

$5\mathrm{.}1$ How many units of each product should Westford produce?

$(12)$

$5\mathrm{.}2$ Calculate the total contribution earned for the optimal production mix.

$(3)$