Inventory Problem

Problem $1-$ You company is planning production of items for the next year. Your demand is given in the following table. Holding inventory cost $$10$ per item month. Setups in a period cost $$100.$ No backorders are allowed.

$\backslash$table$[[\backslash$table$[[$Mont$],[$h$]],1,2,3,4,5,6,7,8,9,10,11,12],[\backslash$table$[[$Dem$],[$and$]],80,30,70,95,100,210,140,100,60,50,32,12]]$

A$.$ Formulate this problem

B$.$ Add constraints to limit the production of items to less than $200$ per month.

C$.$ Add a constraint that forces at least one week off in the period of the $4$ week to $8$ week.