Question $1$

Ding Bakery makes three different tarts from pineapple and flour: Pineapple Tarts, Pineapple Balls, and Nyonya Pineapple Tarts. The demand forecast for next week, percentages of pineapple and flour, and net profit for each product are shown in the following table.

Demand $($kg$)$ Pineapple $\%$ Flour $\%$ Net profit $($$$/$kg$)$

Pineapple Tarts At least $55048$

$52$

Products Pineapple Balls

No more than $15043$

$57$

Nyonya Pineapple Tarts Between $260$ and $31065$

$35$

$271823$

Ding Bakery has $620$ kilograms of pineapple and $510$ kilograms of flour for use next week. These products are made using three different machines. The availability of the machines next week is as follows: $35$ hrs for Machine I, $32$ hrs for Machine II$,$ and $38$ hrs for Machine III. The following table summarises the time required by each product on each machine.

Minutes required per kilogram

Pineapple Tarts

Pineapple Balls Nyonya Pineapple Tarts

Machine I $1\mathrm{.}401\mathrm{.}201\mathrm{.}40$

Machine II $2\mathrm{.}101\mathrm{.}301\mathrm{.}20$

Machine III $1\mathrm{.}100\mathrm{.}800\mathrm{.}60$

Assume you have been tasked to find the production plan that maximises the total profit.

Question $1$a

Formulate an LP model for this problem.

Question $1$b

$(10$ marks$)$

Set up a spreadsheet model for this problem.

Determine the optimal solution using the Solver. Comment on your results. $(20$ marks$)$

Question $1$c

If you want to change the production of any product, which one would you recommend

and why?

$(10$ marks$)$