answer q d please

Question 1 Assume that in the context of a production problem there are two products. P1 and P2 that are manufacture on three machines, M1,M2, and M3. Each product has to be processed on each of the three machines, but order in which the products are processed on the machines is assumed to be immaterial. The two produ sell for the (fixed) unit price of $12 and $27, respectively, while the capacities of the three machines are 14 , and 12 hours, respectively. Note that the capacities are expressed for the planning period, e.g.- one It is important that all other capacity uses are then also expressed in the same units for the same plan period. The different capacities may result from different expected maintenance requirements. No minutes is required to process one unit of unit of P1 on M1,6 minutes to process one unit of P1 on M2, a minutes to process one unit of P1 on M3. The corresponding data for P2 are 12,14 , and 18 . Finally required that at least 70 product units are made and sold. (b) Formulate the problem using linear programming technique objective function: mex.z=12x+22y Subject to {9x+12y15(60) Constraints 9x+12y15(60)6x+14y14(60)10x+18y12(60) Decision variabler: x+y20 Non-negative constraint: x,y0 (d) Solve the model obtained in (c) using graphical method to show the feasible regic portion to show the polytope (Use the graph sheet provided for the solution) 11/hat are the extreme points (feasible set) of the polytope? Question 1 Assume that in the context of a production problem there are two products. P1 and P2 that are manufacture on three machines, M1,M2, and M3. Each product has to be processed on each of the three machines, but order in which the products are processed on the machines is assumed to be immaterial. The two produ sell for the (fixed) unit price of $12 and $27, respectively, while the capacities of the three machines are 14 , and 12 hours, respectively. Note that the capacities are expressed for the planning period, e.g.- one It is important that all other capacity uses are then also expressed in the same units for the same plan period. The different capacities may result from different expected maintenance requirements. No minutes is required to process one unit of unit of P1 on M1,6 minutes to process one unit of P1 on M2, a minutes to process one unit of P1 on M3. The corresponding data for P2 are 12,14 , and 18 . Finally required that at least 70 product units are made and sold. (b) Formulate the problem using linear programming technique objective function: mex.z=12x+22y Subject to {9x+12y15(60) Constraints 9x+12y15(60)6x+14y14(60)10x+18y12(60) Decision variabler: x+y20 Non-negative constraint: x,y0 (d) Solve the model obtained in (c) using graphical method to show the feasible regic portion to show the polytope (Use the graph sheet provided for the solution) 11/hat are the extreme points (feasible set) of the polytope