A carpenter produces orders according to the raw materials available to her For now, she can produce only tables and chairs. She has the option to source $18$ blocks of wood from a walnut tree $($type $1$ wood$)$ and $32$ blocks of wood from an oak tree $($type $2$ wood$)$ to use for crafting these two products. $58\%$ of catch chair is made up of type $2$ wood because some parts need extra rigidity, and $72\%$ of each table is made up of type $1$ wood because the surface requires cottar smoothness. The Oost per block of type $1$ wood is $$7,$ and the cost per block of type $2$ wood is $$5.$ The carpenter has a budget of $$370.$ Due to their textures. each block of type $1$ wood takes half of a shift, and each block of type $2$ wood takes one and a half shifts to be processed. There are $24$ shifts available for the carpenter to craft these products. After that point, she will not be supplied with raw materials used for chair and table production anymore. The profit per chair is $824,$ and per table is $$37.$ Write a linear programming problem to maximize the profit by clearly defining the decision variables, sets, and parameters.