Question $1$

SUSS Engineering Co Ltd is a precision engineering manufacturer that manufactures two

flagship parts for the aerospace sector; Comp $1$ and Comp $2,$ with a profit of $$60$ and $$100$

per piece, respectively.

Comp$1$ and Comp$2$ need to be assembled by a custom$-$made machine $($Machine A$)$ where

it takes $24$ minutes and $50$ minutes to work on Comp$1$ and Comp$2,$ respectively. After the

assembly stage, it needs to be polished and treated by another machine $($Machine B$)$ where

it takes $38$ minutes and $48$ minutes to work on Comp$1$ and Comp$2,$ respectively. The

factory opens for production for $12$ hours daily, on a $5-$day work week. However, due to

maintenance and breakdown, we can assume that both machines are available effectively

$80\%$ of the time. Due to the historical market requirement, for every ten units of Comp$2,$

at most four units of Comp$1$ should be produced.

Question $1$a

Apply linear programming $($LP$)$ model technique by stating the full LP model for the

production problem described above and solve it using the Graphical approach.

$(20$ marks$)$

Question $1$b

Show the maximum amount you would be willing to pay weekly for leasing an extra set of

Machine A and Machine B if the machine vendor offers it for lease.

$(5$ marks$)$