formulate a linear program fot this question

Example: Red Tomato Tools The demand for Red Tomato's gardening tools from consumers is highly seasonal, peaking in the spring as people plant their gardens. Red Tomato has decided to use aggregate planning to overcome the obstacle of seasonal demand maximize 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 Building up a backlog of orders that will be delivered late to customers. Example: Red Tomato Tools The following table summarizes the demand forecast for Red Tomato Tools: Month Demand Forecast January 1600 February 3000 March 3200 April 3800 May 2200 June 2200 Example: Red Tomato Tools The following table summarizes the unit costs for Red Tomato Tools: Item Cost Material cost $10/unit $2/unit/month $5/unit/month $300/worker Inventory holding cost Marginal cost of backlog Hiring/training costs Layoff cost Labor hours required Regular time cost $500/worker 4/unit $4/hour $6/hour Overtime cost. $30/unit Cost of subcontracting Example: Red Tomato Tools Red Tomato sells each tool to the retailers for $40. The company has a starting inventory in January of 1000 tools. At the beginning of January the company has a workforce of 80 employees. The plant has a total of 20 working days in each month, and each employee works eight hours per day on straight time and the rest on overtime. Because of labor rules, no employee works more than 10 hours of overtime per month. Red Tomato has no limits on subcontracting, inventories, and backlog. All stockouts are backlogged and supplied from the following month's production. Inventory costs are incurred on the ending inventory in the month. The supply chain manager's goal is to end June with at least 500 units of inventory. All demand has to be met (even backlogged). Hiring/firing is only possible in the beginning of each month