Do not need a solution, only an optimizatikn model including onjective (minimise cost) and constraints will be fine.

Question 6 (Sales of Operations Planning). [16 points) The All-Colorful Company produces a variety of paint products. Demand is highly seasonal, and the forecasted demand (in gallons) for the next 4 quarters is given as follows: Quarter 1 300,000 Quarter 2 850,000 Quarter 3 1,500,000 Quarter 4 350,000 Demand Forecast The All-Colorful Company has a regular-time production capacity of 90,000 working hours per quarter for Quarters 1, 2, and 4, and the regular-time production capacity of Quarter 3 is 150,000 working hours. Besides regular-time production, the All-Colorful Company can also use overtime production or subcontracting. The maximum overtime working hours in any quarter is 20% of regular-time capacity. Each gallon requires 0.2 working hour of production. The subcontractor can supply a maximum of 200,000 gallons per quarter. The All-Colorful Company has an initial inventory of 250,000 gallons at the beginning of Quarter 1, and the ending inventory at the end of Quarter 4 should be 300,000 gallons. Regular-time cost is $10 per hour, overtime cost is $15 per hour, subcontracting cost is $4 per gallon, and the inventory holding cost is $3 per gallon per quarter. Assume no backorders or stockouts are permitted. Formulate a linear program to determine the best production plan