The ABC Toy Company makes a few types of toy cars on one of its production line. Based on orders received and forecasts of future demand, it is estimated that the demand (in units) for the next four seasons is: Fall 10,000; Winter 8000; Spring 7,000; Summer 12,000. Inventory at the beginning of Fall is 660 units. At the beginning of Fall, ABC has 30 workers. Relevant costs: hiring: $100/worker hired layoff: $200/worker laid off inventory holding: $5/unit/season backorder: $10/unit regular time cost: $5/hour Assume that the productivity is 0.5 units per worker hour, with eight hours per day and 60 days per season. Inventory cost is estimated based on the ending inventory for each period. The relevant costs are shown in the accompanying table. (a) Find the total cost of the level plan. (b) Find the total cost of the chase plan. (c) Suppose that ABC has negotiated with the union on the option of using the regular workforce on overtime ($8/hour) during Winter and Spring, if necessary. Overtime is not available for the other seasons. The new company policy restricts hiring (or firing) to take place only once a year. Consequently, it is decided that hiring takes places only in the beginning of Summer while firing can be done at the end of Summer. Formulate the problem as a linear program. Be sure to define all the variables.