Remarks & Instructions: 1. Do not scale any coefficient or function. All coefficients must be numeric values. 2. Right-hand side of each constraint should be a nonnegative numeric value. 3. Do not put any spaces, extra characters or explanations since these may render your answer incorrect. 4. An empty box is considered incorrect and receives zero point. A company produces a single type of product. The product sells for $6 per unit. The customer demands must be met on time. Monthly demands for the product, production and holding costs, and production capacities are shown in the table below. Demand Holding cost Production cost Production capacity Month (units) ($/unit/month) ($/unit) (units) M1 55 0.1 1.5 65 M2 45 0.18 1.6 85 M3 115 0.21 1.7 105 At the beginning of month 1, the company has 6 units of the product in inventory. For the decision variables, assume that t shows the month (1,2,3), xt is the quantity produced in month t, It is the inventory left over at the end of month t. The company wants at least 4 units in inventory at the end of each month. We would like to maximize the total profit during three months (M1, M2, M3) for this problem using an integer program. A partial mathematical model is given below. Fill the boxes accordingly. x1+ x2+ X3+ 11+ 12 + 13 (Objective & Objective Function) s.t. x1+ x2+ X3+ 11+ 12+ 13 (M2 capacity) X1+ X2+ x3+ 11+ 12+ 13 (M1 inventory balance) x1+ x2+ x3+ 11+ 12+ 13 (M3 inventory balance) x1+ x2+ X3+ 11+ 12+ 13 (M2 ending inventory requirement) x1, x2, x3 (Sign/type restrictions) 11, 12, 13 (Sign/type restrictions)