The workload for a local job shop is subject to considerable fluctuations throughout the year. However, machine operators are difficult to hire and costly to train, so the manager is reluctant to lay off workers during the slack seasons (slack season > time period wherein sales is lower as compared to the average). He is likewise reluctant to maintain his peak season (peak season > time period wherein sales is higher as compared to the average) payroll when it is not required. Furthermore, he is definitely opposed to overtime work on a regular basis. Since all work is done to custom orders, it is not possible to build up inventories during slack seasons. Therefore, the manager is in a dilemma as to what his policy should be regarding employment levels.

The following estimates are given for the minimum employment requirements during the next three quarters of 2010 and the first two quarters of 2011:

Quarter = 2Q '10 = 3Q '10 = 4Q '10 = 1Q '10 = 2Q '10

Requirements = 25 = 22 = 24 = 20 = 26

Employment will not be permitted to fall below these levels. Any employment above these levels is wasted at an approximate cost of PhP100,000 per person per quarter. It is estimated that both hiring and firing costs are PhP10,000 times the square of the difference between the current and previous quarter employment levels (Ex. If in 2Q '10 you had 25 workers and you decide to maintain only 22 workers in 3Q '10, the cost of firing will be 10,000x (25-22)² = 90,000).

Determine the number of workers to be hired for each of the five quarters to minimize hiring cost.