we should use python to solve it

The constraints of the problem can be determined directly from the representation in Figure For each period we have the following balance equation: Beginning inventory + Production amount - Ending inventory = Demand This is translated mathematically for the individual months as x1I1=100I1+x2I2=250I2+x3I3=190I3+x4I4=140I4+x5I5=220(Month5)I5+x6=110(Month6)x1,i=1,2,,6,Il0,i=1,2,.5(Month1)(Month2)(Month3)(Month4) Note that the initial inventory, I0, is zero. Also, in any optimal solution, the ending inventory I6 will be zero because it is not economical to incur unnecessary additional storage cost. Optimum solution: Solution: The optimum solution (obtained using file amplEx2.4-3.trt) is summarized in Figure 2.10. It shows that each month's demand is satisfied from the same month's production, except for month 2 where the production quantity ( =440 units) covers the demand for both months 2 and 3. The total associated cost is z=$49,980. Objective: The objective of this exercise is to enable the students to build their production planning optimization model in CPLEX software in a structured method. Instructions: Divide your CPLEX model into three parts: 1. Parameter section: Definition of variables types, names, sizes, and the input data for these variables should be defined. 2. Decision variables section: Definition of decision variables types, names, and sizes performed in this stage. 3. Model Section: Objective function and constrains are defined in this stage. Example: "Multiole Period Production-Inventorv Model" from Hamdv Taha book. Ch. 2. examole 2.4-3 Acme Manufacturing Company has a contract to deliver 100,250,190,140,220, and 110 home windows over the next 6 months. Production cost (labor, material, and utilities) per window varies by period and is estimated to be $50,$45,$55,$48,$52, and $50 over the next 6 months. To take advantage of the fluctuations in manufacturing cost, Acme can produce more windows than needed in a given month and hold the extra units for delivery in later months. This will incur a storage cost at the rate of $8 per window per month, assessed on end-of-month inventory. Develop a linear program to determine the optimum production schedule. Mathematical Model: The variables of the problem include the monthly production amount and the end-of-month inventory. For i=1,2,,6, let xi= Number of units produced in month i Ii= Inventory units left at the end of month i The relationship between these variables and the monthly demand over the 6-month horizon is represented schematically in Figure 2.9. The system starts empty (I0=0). The objective is to minimize the total cost of production and end-of-month inventory. Total production cost =50x1+45x2+55x3+48x4+52x5+50x6 Total inventory (storage) cost =8(I1+I2+I3+I4+I5+I6) Thus the objective function is Minimizez=50x1+45x2+55x3+48x4+52x5+50x6+8(I1+I2+I3+I4+I5+I6) The constraints of the problem can be determined directly from the representation in Figure For each period we have the following balance equation: Beginning inventory + Production amount - Ending inventory = Demand This is translated mathematically for the individual months as x1I1=100I1+x2I2=250I2+x3I3=190I3+x4I4=140I4+x5I5=220(Month5)I5+x6=110(Month6)x1,i=1,2,,6,Il0,i=1,2,.5(Month1)(Month2)(Month3)(Month4) Note that the initial inventory, I0, is zero. Also, in any optimal solution, the ending inventory I6 will be zero because it is not economical to incur unnecessary additional storage cost. Optimum solution: Solution: The optimum solution (obtained using file amplEx2.4-3.trt) is summarized in Figure 2.10. It shows that each month's demand is satisfied from the same month's production, except for month 2 where the production quantity ( =440 units) covers the demand for both months 2 and 3. The total associated cost is z=$49,980. Objective: The objective of this exercise is to enable the students to build their production planning optimization model in CPLEX software in a structured method. Instructions: Divide your CPLEX model into three parts: 1. Parameter section: Definition of variables types, names, sizes, and the input data for these variables should be defined. 2. Decision variables section: Definition of decision variables types, names, and sizes performed in this stage. 3. Model Section: Objective function and constrains are defined in this stage. Example: "Multiole Period Production-Inventorv Model" from Hamdv Taha book. Ch. 2. examole 2.4-3 Acme Manufacturing Company has a contract to deliver 100,250,190,140,220, and 110 home windows over the next 6 months. Production cost (labor, material, and utilities) per window varies by period and is estimated to be $50,$45,$55,$48,$52, and $50 over the next 6 months. To take advantage of the fluctuations in manufacturing cost, Acme can produce more windows than needed in a given month and hold the extra units for delivery in later months. This will incur a storage cost at the rate of $8 per window per month, assessed on end-of-month inventory. Develop a linear program to determine the optimum production schedule. Mathematical Model: The variables of the problem include the monthly production amount and the end-of-month inventory. For i=1,2,,6, let xi= Number of units produced in month i Ii= Inventory units left at the end of month i The relationship between these variables and the monthly demand over the 6-month horizon is represented schematically in Figure 2.9. The system starts empty (I0=0). The objective is to minimize the total cost of production and end-of-month inventory. Total production cost =50x1+45x2+55x3+48x4+52x5+50x6 Total inventory (storage) cost =8(I1+I2+I3+I4+I5+I6) Thus the objective function is Minimizez=50x1+45x2+55x3+48x4+52x5+50x6+8(I1+I2+I3+I4+I5+I6)