LP Applications

Problems with more than $2$ variables

Example $2\mathrm{.}4-2($Single$-$Period Production Model$)$

In preparation for the winter season, a clothing company is manufacturing parka and goose overcoats, insulated pants, and gloves. All products are manufactured in four different departments: cutting, insulating, sewing, and packaging. The company has received firm orders for its products. The contract stipulates a penalty for undelivered items. Devise an optimal production plan for the company based on the followine data:

$\backslash$table$[[$Departmeat$,$Time per unit $($hr$),$Capacity $($hr$)],[$Arrka$,$Goose,Rants,Gloves$],[$Cutting$,30,30,25,15,1000],[$Insulating$,\mathrm{.}25,35,30,10,1000],[$Scwing$,\mathrm{.}45,50,40,22,1000],[$Packaging$,\mathrm{.}15,15,.t,85,1000],[$Dcmand$,800,750,600,500,.],[$Unit profit,$530,$$$40,520,$$$10,],[$Unit penalty,$$15,$$$20,$$$10,58,]]$