Question 3: Linear Programming Formulation (22 points) The ABC Company produces backpacks for everyday use. ABC must decide how many backpacks to produce each month. The company has decided to use a 6-month planning horizon. The forecasted demands for the next six months are 15,000, 18,000, 25,000, 30,000, 20,000 and 12,000. ABC wants to meet these demands on time, knowing that it currently has 5,000 backpacks in inventory and that it can use a given month's production to help meet the demand for that month. (For simplicity we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 backpacks, and there is enough storage capacity to store up to 10,000 at the end of the month, after demand has occurred. The forecasted production costs per backpack for the next six months are $15.50, $15.55, $15.70, $15.80, $15.85, and $15.95, respectively. The holding cost per backpack held in inventory at the end of any month is figured at 5% of the production cost for that month. (This cost includes the cost of storage and the cost of money tied up in inventory.) The price of backpacks is not considered relevant to the production decision because ABC will satisfy all customer demand exactly when it occurs at whatever the selling price is. Therefore, ABC wants to determine the production schedule that minimizes the total production and holding costs. Develop an LP model to find the production schedule that meets demand on time and minimizes total production and inventory holding costs. Define the decision variables, objective function, and constraints. DO NOT SOLVE. Hint: Drawing a visual aid may help to better understand the