1)Production Planning The Portland company, the Weatherman, makes a single, very specialized multipurpose tool. Demand for the next four quarters is known to be 700, 1200, 550, and 1000 units respectively. The production cost is $1250 per unit. The per unit cost to hold one unit in inventory is 25% of the production cost per quarter. An inventory buffer of 25 units must be maintained at the end of every quarter (including at the end of the planning horizon) for warranty issues and other purposes. Due to production capacity limitations, no more than 1000 units can be produced in any quarter. At the beginning of the planning, there are 30 units in inventory. 1.1 Formulate an explicit mathematical optimization model for this problem using LaTeX in RMarkdown. 1.2 Implement and solve your optimization model using ompr. 1.3 Interpret and discuss the solution to the problem. 1.4 Modified Example Formulation Weatherman is looking at investing in a manufacturing process that will decrease their manufacturing cost per item to $1100 per unit. Production capacity would increase to 2000 units per quarter but there is a setup cost of $5000 each quarter in which units are produced. Cre ate a new optimization formulation for this modified situation 1.5 Implement and Solve the modified model. Discuss the results 1.6 Compare the results between the models in light of managerial insights