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.

Pineapple Tarts

Demand $($kg$)$ at least $550$ kg

Pineapple percentage $48\%$

Flour percentage $52\%$

Net profit $($$$/$kg$)-$ $$27/$kg

Pineapple Balls

Demand $($kg$)$ no more than $150$ kg

Pineapple percentage $43\%$

Flour percentage $57\%$

Net profit $($$$/$kg$)-$ $$18/$kg

Nyonya Pineapple Tarts

Demand $($kg$)$ Between $260$ and $310$ kg

Pineapple percentage $65\%$

Flour percentage $35\%$

Net profit $($$$/$kg$)-$ $$23/$kg

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 $($mins $/$ kg$)$

Pineapple Tarts

Machine $11\mathrm{.}40$ mins $/$ kg

Machine $21\mathrm{.}20$ mins $/$ kg

Machine $31\mathrm{.}40$ mins $/$ kg

Pineapple Balls

Machine $12\mathrm{.}10$ mins $/$ kg

Machine $21\mathrm{.}30$ mins $/$ kg

Machine $31\mathrm{.}20$ mins $/$ kg

Nyonya Pineapple Tarts

Machine $11\mathrm{.}10$ mins $/$ kg

Machine $20\mathrm{.}80$ mins $/$ kg

Machine $30\mathrm{.}60$ mins $/$ kg

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

Formulate an LP model for this problem.

Set up a spreadsheet model for this problem. Determine the optimal solution using the Solver. Comment on your results.

If you want to change the production of any product, which one would you recommend and why?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.

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, $32hrs$ for Machine II$,$ and $38$

hrs for Machine III. The following table summarises the time required by each product

on each machine.

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.

$(10$ marks$)$

Question $1$b

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$)$