Section A $(100$ marks$)$

Answer all questions in this section.

Question $1$

Company XYZ is a high$-$end, bespoke shoemaker. They only produce $3$ different types

of shoe models: Alpha, Beta and Gamma. Their production volume is low as the process

to finish the shoes is long and tedious. The production team operates on a five$-$day

week. The bottleneck of the shoemaking process occurs at the last two stages where it

needs to be completed by Machine A and Machine B with the following time

requirement per pair of shoes:

Table $1\mathrm{.}1$

The available daily capacity for Machine A and Machine B is $21$ hours and $3$ hours,

respectively.

The weekly supply of leather is $29,200$ units and the amount of leather required to make

each pair of shoes is as follows:

The sales team has provided the following demand information for the past five weeks:

The profit for each pair of shoe model Alpha, Beta and Gamma is $$450,$$$900$ and $$800,$

respectively. However, if the shoemaker is not able to meet the weekly forecast demand

in Week $6,$ each pair of unfulfilled demand will result in loss of goodwill and that

translates to a cost of $$100,$$$200$ and $$100$ for shoe model Alpha, Beta and Gamma,

respectively. Further, no leftover shoes are allowed.

Figure $1\mathrm{.}1$ shows the output from EXCEL Solver after it has been developed using

Linear Programming and solved.

Variable Cells

Figure $1\mathrm{.}1$

Question $1$a

Use the $3-$week moving average model to predict the weekly demand for each of the

shoe model for Week $6.$ Then apply linear programming $($LP$)$ by formulating the

production problem for Week $6.$

$(17$ marks$)$

Question $1$b

Using Figure $1\mathrm{.}1,$ state the optimal production quantity. Recommend a feasible and

realistic production quantity in Week $6.$ You are required to show your workings

leading to your recommendation.

$(8$ marks$)$