$[20$ points$]$ A pallet with a dimension of $(1200$ mm x $1000$ mm x $150$ mm$)($Length x Width x Height$)$ is used to store cartons, each measuring $250$ mm x $200$ mm x $150$ mm $($Length x Width x Height$)$ and weighs $1\mathrm{.}5$ kg$.$ The loaded pallets are stored in a rack with a clearance height of $2100$ mm$.$ To handle the loaded pallets, a clearance of $150$ mm is required between the top of the pallet and the underside of the beam. Assume that the cartons are sturdy and can be stacked without crushing the bottom layer. Also, the cartons can be oriented in any direction.

a$.$ How many pallets would fit on the pallet for one layer? Show all calculations.

b$.$ How many pallets can be stacked on the pallet such that it can be stored on the rack $($adhering to the available clearance$)?$ Show all calculations.

c$.$ How much would the loaded pallet weigh? $($You may confirm your answers with the online tool$).$

d$.$ If there is a weight limit of $300$ kgs for one pallet, does the number of pallets stacked on the pallet change? Why or why not?

e$.$ If the maximum top load a carton can carry is $10$ kg$,$ how ma