Project your own thermal cup$/$mug$,$ based on professional models and existing patents. You should determine its geometry, dimensions, materials. The requirements are: a$.$ Total volume $($dimension$)$ cannot exceed $1\mathrm{.}5$ L b$.$ Should hold at least $300$ mL of liquid c$.$ Cannot weigh more than $700$ g d$.$ Should be $$liquid proof$,$ i$.$e$.,$ cannot leak or deteriorate when in contact with liquids. e$.$ Should keep contents at a temperature higher or equal to $55\%$ of the original temperature for at least $3$ hours. f$.$ Aesthetics will not be marked $2)$ Sketch your project $($manually or using software$),$ justify through references or calculations the choosing of the geometry, dimensions and materials, display $($or estimate$)$ all the thermal conductivity $($k$)$ involved $3)$ Estimate the price your thermo would cost. That is$,$ the manufacturing price $($design$,$ materials, labour, equipment, etc.$).$ Note this is NOT the retail price. $*4)$ Calculate the expected heat transfer and the expected energy loss over a period of $3$ hours and show that your envisioned product is capable of keeping liquid inside at a temperature higher or equal to $55\%$ of the original temperature for $3$ hours in a city like Sydney. $*$