Question $2$

$20$

$2\mathrm{.}1$ The D & E Groups manufactures two electrical products: Product A and Product B$.$ both products undergo assembly process of wiring and drilling. Each Product A takes $3$ hours of wiring and $2$ hours of drilling. Each Product B must go through $2$ hours of wiring and $1$ hour of drilling. During the next production period, $240$ hours of wiring time are available, and up to $140$ hours of drilling time may be used. Each Product A sold yields a profit of R$25\mathrm{.}00.$ Each Product B assembled may be sold for a R$15$ profit.

I. Formulate and solve this LP production mix situation.

II$.$ Find the best combination of Product A and Product B that yields the highest profit using the corner point graphical approach.

$2\mathrm{.}2.D$ and $E$ Groups' management realizes that it forgot to include two critical constraints. Management decides that there should be a minimum number of Product A produced to fulfil a contract. Also, due to an oversupply of Product B in the preceding period, a limit should be placed on the total number of Product B produced.

$2\mathrm{.}2\mathrm{.}1$ If $D$&$E$ groups decides that at least $20$ Product A should be produced but no more than $80$ Product $B$ should be produced.

I. What would be the optimal solution?

II$.$ How much slack or surplus is there for each of the four constraints?

$2\mathrm{.}2\mathrm{.}2$ If $D$ & $E$ groups decides that at least $30$ Product A should be produced but no more than $50$ Product $B$ should be produced.

I. What would be the optimal solution?

II$.$ How much slack or surplus is there for each of the four constraints at the optimal solution?