Solve part f and g. provide step by step answer in details

7.2-8. Consider the following problem. Maximize Z=c1x1+c2c2. subject to 2x1x2b1x1x2b2 and x10.x20. Let x3 and x4 denote the slack variables for the respective functional constraints. When c1=3,c2=2,b1=30, and b2=10, the simplex method yields the following final simplex tablenu. I (a) Use graphical analysis to determine the allowable range for c1 and c2. (b) Use algebraic analysis to derive and verify your answers in part (a). 1 (c) Use graphical analysis to determine the allowable range for b1 and b2. (d) Use algebraic analysis to derive and verify your answers in part (c) C. (e) Use a software package based on the simplex method to find these allowable ranges. Part (f): Using the 100% rule and the ranges you found earlier, make a conclusion as to Whether the current optimal solution remains optimal or not, if c1=3.5 and c2=1.75. Verify your answer by solving the problem with the new objective coefficients using a software. Part (g): By directly evaluating the parametric expressions found in part (b), determine the shadow prices of the resources and the optimal objective value if the unit profit of activity 1 increases by . 5 (all other parameters are unchanged). Similarly, using the parametric expressions found in part (d), determine the optimal activity levels and profit if the second resource amount decreases by 3 units lall other parameters are unchanged). 7.2-8. Consider the following problem. Maximize Z=c1x1+c2c2. subject to 2x1x2b1x1x2b2 and x10.x20. Let x3 and x4 denote the slack variables for the respective functional constraints. When c1=3,c2=2,b1=30, and b2=10, the simplex method yields the following final simplex tablenu. I (a) Use graphical analysis to determine the allowable range for c1 and c2. (b) Use algebraic analysis to derive and verify your answers in part (a). 1 (c) Use graphical analysis to determine the allowable range for b1 and b2. (d) Use algebraic analysis to derive and verify your answers in part (c) C. (e) Use a software package based on the simplex method to find these allowable ranges. Part (f): Using the 100% rule and the ranges you found earlier, make a conclusion as to Whether the current optimal solution remains optimal or not, if c1=3.5 and c2=1.75. Verify your answer by solving the problem with the new objective coefficients using a software. Part (g): By directly evaluating the parametric expressions found in part (b), determine the shadow prices of the resources and the optimal objective value if the unit profit of activity 1 increases by . 5 (all other parameters are unchanged). Similarly, using the parametric expressions found in part (d), determine the optimal activity levels and profit if the second resource amount decreases by 3 units lall other parameters are unchanged)