Problem 8.0.3 (Problem 20 (page 407) in text[1]:) Filtron corporation produces filtration containers used in water treatment systems. Although business has been growing, the de- mand each month varies considerably. As a result, the company utilizes a mix of part-time and full-time employees to meet production demands. Although this approach provides Filtron with great flexibility, it resulted in increased costs and morale problems among em- ployees. For instance, if Filtron needs to increase production from one month to the next, additional part-time employees have to be hired and trained, and costs go up. If Filtron has to decrease production, the workforce has to be reduced and Filtron incurs additional costs in terms of unemployment benefits and decreased morale. Best estimates are that in- creasing the number of units produced from one month to the next will increase production costs by $1.25 per unit, and that decreasing the number of units produced will increase pro- duction costs by $1 per unit. In February Filtron produced 10000 filtration containers but only sole 7500 units; 2500 units are currently in inventory. The sales forecasts for March, April and May are for 12000 units, 8000 units and 15000 units, respectively. In addition, Filtron has the capacity to store up to 3000 filtration containers at the end of any month. Management would like to determine the number of units to be produced in March, April and May that will minimize the total cost of the monthly production increases and decreases.