Linear Programming — Multiperiod Inventory Problem

Ryan Howe
5 min readJul 31, 2021

The following is meant to continue some of the work I had been doing in these two articles I wrote ( and


In these articles I introduced some basic ideas about linear programming models using some fictional water plant. The original problems are in block quotes below.

Problem 1

Geg table water factory produces types of water, namely, MG and HJ. Products are produced and sold on a weekly basis. The weekly production cannot exceed 50 for MG. And 70 for HJ because of limitations within factory. The company employed 120 workers. MG water production requires 2 man hour weeks of labor while HJ requires 1 man hour week of labor. Profit margin on MG is $120 and on HJ is $80.

Problem 2

In this case we’ll be looking at a company which has two factories, factory A and factory B. The company makes bearings and produces two products which we’ll call grade I and grade II. Each of these produces a different profit, grade I makes $10 and grade II makes $12. The company gets a certain amount of raw material every week (here we’ll say 100 lbs) and splits it between the plants.

Factory A will get 60 units and factory B gets 40 units. Now it takes 4 lbs to produce each bearing. They grind the bearings and…