How to solve this in GAMS? There are already solutions on chegg in excel but I need it coded in GAMS.
Table 1 below shows monthly demand forecast for a company's products. The company needs to meet the demand and end December with at least 700 tools (i.e., no stockouts at the end of December and at least 700 tools in inventory). At the beginning of January the company has a workforce of 50 employees and 1000 tools in inventory. The material cost for each tool is $10. The company has a total of 20 working days in each month, and each employee earns $15 per hour regular time and $20 per hour overtime. Each employee works eight hours per day on regular time and the rest on overtime. No employee works more than 10 hours of overtime each month. Each employee can produce 40 tools per month on regular time and one tool for every four hours of overtime. At the beginning of each month, the company decides how many additional employees are hired or how many current employees are laid off. The cost of hiring an employee is $300 and the cost of laying off an employee is $400. To meet the demand, the company can build up inventory during the slow months (i.e., months in which the demand is low) or building up a backlog of orders (stockouts) that will be delivered late to customers. The cost of carrying inventory is $2 per tool per month, and the cost of stocking out is $3 per tool per month. In addition to manufacturing tools in its facility, the company can subcontract out some of the work. The subcontracting cost is $70/tool. (i.e., the company can purchase one tool at $70 from suppliers to meet the demand.) Please formulate an LP to help the company minimize the total cost. Please use GAMS to find the optimal solution and optimal value. Table 1. Monthly Demand Forecast Month Demand Forecast Number of Tools Januar Februar March April June 2000 1500 800 2400 2000 Month Demand Forecast Number of Tools Jul August SeptemberOctoberNovemberDecember 1750 2800 900 3500 4000 2000 Table 1 below shows monthly demand forecast for a company's products. The company needs to meet the demand and end December with at least 700 tools (i.e., no stockouts at the end of December and at least 700 tools in inventory). At the beginning of January the company has a workforce of 50 employees and 1000 tools in inventory. The material cost for each tool is $10. The company has a total of 20 working days in each month, and each employee earns $15 per hour regular time and $20 per hour overtime. Each employee works eight hours per day on regular time and the rest on overtime. No employee works more than 10 hours of overtime each month. Each employee can produce 40 tools per month on regular time and one tool for every four hours of overtime. At the beginning of each month, the company decides how many additional employees are hired or how many current employees are laid off. The cost of hiring an employee is $300 and the cost of laying off an employee is $400. To meet the demand, the company can build up inventory during the slow months (i.e., months in which the demand is low) or building up a backlog of orders (stockouts) that will be delivered late to customers. The cost of carrying inventory is $2 per tool per month, and the cost of stocking out is $3 per tool per month. In addition to manufacturing tools in its facility, the company can subcontract out some of the work. The subcontracting cost is $70/tool. (i.e., the company can purchase one tool at $70 from suppliers to meet the demand.) Please formulate an LP to help the company minimize the total cost. Please use GAMS to find the optimal solution and optimal value. Table 1. Monthly Demand Forecast Month Demand Forecast Number of Tools Januar Februar March April June 2000 1500 800 2400 2000 Month Demand Forecast Number of Tools Jul August SeptemberOctoberNovemberDecember 1750 2800 900 3500 4000 2000
