The demand for Red Tomato Tools gardening tools is highly seasonal, peaking in the summer when people plant their gardens. Red Tomato has decided to use aggregate planning to overcome this obstacle of seasonal demand and maximize their profits. The options Red Tomato has for handling the seasonality are adding workers during the peak season, subcontracting out some of the work, building up inventory during the slow months and building up backlog of orders that will be delivered late to customers. To determine how to best use these options through an aggregate plan, Red Tomatos VP for Supply Chain Operations starts with demand forecasts for its tools over the next six months. These are shown in the following table

a) SCENARIO 1: The demand for Red Tomato Tools gardening tools is highly seasonal, peaking in the summer when people plant their gardens. Red Tomato has decided to use aggregate planning to overcome this obstacle of seasonal demand and maximize their profits. The options Red Tomato has for handling the seasonality are adding workers during the peak season, subcontracting out some of the work, building up inventory during the slow months and building up backlog of orders that will be delivered late to customers. To determine how to best use these options through an aggregate plan, Red Tomato's VP for Supply Chain Operations starts with demand forecasts for its tools over the next six months. These are shown in the following table. Demand Forecast Month January 1,600 February 3,000 March 3,200 April 3,800 May 2,200 June 2,200 Red Tomato sells each tool to retailers for $40. The company has a starting inventory in January of 1,000 tools. At the beginning of January, the company has a workforce of 80 employees. The plant has a total of 20 working days each month, and each employee earns $4.00 per hour regular time. Each employee works a total of eight hours a day on straight time and the rest on overtime. The capacity of the production operation is determined primarily by the total labor hours worked. Due to labor rules, no employee works more than 10 hours of overtime per month. Each tool needs 4 work hours. Other costs are shown in the following table. Item Cost $10/unit Material Cost Inventory Holding Cost $2/unit/month Marginal Cost of Stockout/Backlog $5/unit/month Hiring and Training Costs $300/worker Layoff Cost $500/worker Labor Hours Required 4/unit Regular Time Cost $4/hour Overtime Cost $6/hour $30/unit Cost of Subcontracting Currently, Red Tomato has no limits on subcontracting, inventories, and stock-outs/backlogs. All stock- outs are backlogged and supplied from the following month's production. Inventory costs are incurred on the ending inventory in the month. The supply chain planner's goal is to obtain the optimal aggregate plan that allows Red Tomato to end June with at least 500 units which means no stock-outs at the end of June and at least 500 units of inventory. The optimal aggregate plan is one that results in the highest profit over the six-month planning horizon. Given Red Tomato's desire for a very high level of customer service, we will assume all demand is met. Therefore, revenues earned over the planning horizon are fixed given the fixed price. In this case, minimizing cost over the planning horizon is the same as maximizing profit. b) SCENARIO 2: All the data are exactly the same as in our previous discussion of Red Tomato, except for the demand forecast. Assume that the same overall demand (16,000 units) is distributed over the six months in such a way that the seasonal fluctuation of demand is higher, as shown in the following table. Demand Forecast Month January 1,000 February 3,000 March 3,800 April 4,800 May 2,000 June 1,400 Obtain the optimal aggregate plan in this case. c) SCENARIO 3: Assume that demand at Red Tomato is as shown in the above table (scenario 2), and all other data are the same except holding cost per unit increases from $2 per unit per month to $6 per unit per month. Evaluate the total cost corresponding to the aggregate plan and suggest an optimal aggregate plan for the new cost structure. a) SCENARIO 1: The demand for Red Tomato Tools gardening tools is highly seasonal, peaking in the summer when people plant their gardens. Red Tomato has decided to use aggregate planning to overcome this obstacle of seasonal demand and maximize their profits. The options Red Tomato has for handling the seasonality are adding workers during the peak season, subcontracting out some of the work, building up inventory during the slow months and building up backlog of orders that will be delivered late to customers. To determine how to best use these options through an aggregate plan, Red Tomato's VP for Supply Chain Operations starts with demand forecasts for its tools over the next six months. These are shown in the following table. Demand Forecast Month January 1,600 February 3,000 March 3,200 April 3,800 May 2,200 June 2,200 Red Tomato sells each tool to retailers for $40. The company has a starting inventory in January of 1,000 tools. At the beginning of January, the company has a workforce of 80 employees. The plant has a total of 20 working days each month, and each employee earns $4.00 per hour regular time. Each employee works a total of eight hours a day on straight time and the rest on overtime. The capacity of the production operation is determined primarily by the total labor hours worked. Due to labor rules, no employee works more than 10 hours of overtime per month. Each tool needs 4 work hours. Other costs are shown in the following table. Item Cost $10/unit Material Cost Inventory Holding Cost $2/unit/month Marginal Cost of Stockout/Backlog $5/unit/month Hiring and Training Costs $300/worker Layoff Cost $500/worker Labor Hours Required 4/unit Regular Time Cost $4/hour Overtime Cost $6/hour $30/unit Cost of Subcontracting Currently, Red Tomato has no limits on subcontracting, inventories, and stock-outs/backlogs. All stock- outs are backlogged and supplied from the following month's production. Inventory costs are incurred on the ending inventory in the month. The supply chain planner's goal is to obtain the optimal aggregate plan that allows Red Tomato to end June with at least 500 units which means no stock-outs at the end of June and at least 500 units of inventory. The optimal aggregate plan is one that results in the highest profit over the six-month planning horizon. Given Red Tomato's desire for a very high level of customer service, we will assume all demand is met. Therefore, revenues earned over the planning horizon are fixed given the fixed price. In this case, minimizing cost over the planning horizon is the same as maximizing profit. b) SCENARIO 2: All the data are exactly the same as in our previous discussion of Red Tomato, except for the demand forecast. Assume that the same overall demand (16,000 units) is distributed over the six months in such a way that the seasonal fluctuation of demand is higher, as shown in the following table. Demand Forecast Month January 1,000 February 3,000 March 3,800 April 4,800 May 2,000 June 1,400 Obtain the optimal aggregate plan in this case. c) SCENARIO 3: Assume that demand at Red Tomato is as shown in the above table (scenario 2), and all other data are the same except holding cost per unit increases from $2 per unit per month to $6 per unit per month. Evaluate the total cost corresponding to the aggregate plan and suggest an optimal aggregate plan for the new cost structure