$\backslash$table$[[$Week$,\backslash$table$[[$Demand$],[$Military$],[$backpacks$]],\backslash$table$[[$Demand$],[$College$],[$backpacks$]]],[1,360,210],[2,310,198],[3,325,225],[4,355,230]]$Rocky Mountain Backpacks $($RMB$)$ produce two kinds of products, military backpacks, and college backpacks. The demand for military backpacks and college backpacks for the next $4$ weeks is given in Table $1.$ RMB can produce $510$ military backpacks per week and $600$ college backpacks per week. It costs $$100$ to produce one military backpack and $$60.$ to produce one college backpack. The company's policy on inventory and backorder is as follows:

A$.$ The company cannot have backpacks in the inventory of any type for more than $2$ weeks. The cost of having any type of backpack in inventory is $$2$ per backpack per week.

b$.$ Backorders $($orders that are fulfilled late$)$ is allowed for only $1$ week. The cost of having any type of backpack in backorder is $$3$ per backpack per week. There are currently $32$ military backpacks and $15$ college backpacks in inventory at week $1($leftover from the previous week$).$

C$.$ there are currently $32$ military backpacks and $15$ college backpacks in inventory a week$1($leftover previous week$).$

RMB management wants to plan their production schedule for the next $4$ weeks. Formulate an LP that optimizes the number of backpacks of each type produced per week for the next $4$ weeks while minimizing the costs associated with production, inventory, and backorders. Do all parts please!!