Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 23

In Problem, suppose that the demand for personal computers increased each month, as follows:
In addition to the regular production capacity of 300 units per month, PM Computer Services can also produce an additional 200 computers per month by using overtime. Overtime production adds 20% to the cost of a personal computer.
Determine a production schedule for PM that will minimize total cost.
Problem
PM Computer Services produces personal computers from component parts it buys on the open market. The company can produce a maximum of 300 personal computers per month. PM wants to determine its production schedule for the first 6 months of the new year. The cost to produce a personal computer in January will be $1,200. However, PM knows the cost of component parts will decline each month so that the overall cost to produce a PC will be 5% less each month. The cost of holding a computer in inventory is $15 per unit per month. Following is the demand for the company's computers each month:
Determine a production schedule for PM that will minimize total cost.