Red Tomato sells each tool through retailers for $40. The company has a starting inventory in January of 1,000 tools. At the beginning of January, the company has a work- force of 80 employees. The plant has a total of 20 working days in each month, and each employee earns $4 per hour regular time. Each employee works eight hours per day on straight time and the rest on overtime. As discussed previously, the capacity of the produc- tion operation is determined primarily by the total labor hours worked. Therefore, machine capacity does not limit the capacity of the production operation. Because of labor rules, no employee works more than 10 hours of overtime per month. The various costs are shown in Table 8-3. It is important that the costs and labor hours are in aggregate units, as discussed in Section 8.2. Currently, Red Tomato has no limits on subcontracting, inventories, and stockouts/ backlog. All stockouts are backlogged and supplied from the following months' production. Inventory costs are incurred on the ending inventory in the month. The supply chain manager's goal is to obtain the optimal aggregate plan that allows Red Tomato to end June with at least 500 units (i.e., no stockouts at the end of June and at least 500 units in inventory). The optimal aggregate plan is one that results in the highest profit over the 6-month planning horizon. For now, given Red Tomato's desire for a high level of customer service, assume all demand is to be met, although it can be met late. Therefore, the revenues earned over the planning horizon are fixed. As a result, minimizing cost over the planning horizon is the same as maximizing profit. In many instances, a company has the option of not meeting certain demand, or price itself may be a variable that a company must determine based on the aggregate plan. In such a scenario, minimizing cost is not equivalent to maximizing profits. In the next two sections, we discuss methodologies commonly used for aggregate plan- ning. (Readers who are unfamiliar with linear programming can directly jump to Section 8.6.)