Introduction

Linear programming $($LP$)$ offers a wide array of applications in production planning and inventory control. This lab provides as a tutorial for building a production planning optimization model using Excel.

Problem Statement:

"Single period production Planning" from Hamdy Taha book, CH$2,$ example: $2\mathrm{.}4-2$

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 packing. 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 following data:

$\backslash$table$[[,$Time per unit $($hr$),],[$Department$,$Parka,Goose,Pants,Gloves,Capacity $($hr$)],[$Cutting$,\mathrm{.}30,\mathrm{.}30,\mathrm{.}25,\mathrm{.}15,1000],[$Insulating$,\mathrm{.}25,\mathrm{.}35,\mathrm{.}30,\mathrm{.}10,1000],[$Sewing$,\mathrm{.}45,\mathrm{.}50,\mathrm{.}40,\mathrm{.}22,1000],[$Packaging$,\mathrm{.}15,\mathrm{.}15,\mathrm{.}1,\mathrm{.}05,1000],[$Demand$,800,750,600,500,],[$Unit profit,$$30,$$$40,$$$20,$$$10,],[$Unit penalty,$$15,$$$20,$$$10,$$$8,]]$

$*$using excel $*$