Hi, everybody, I would like to ask you guys a little question. I have three maximization problems, they are Q1, Q2 and Q3, respectively, as you can see below:
Clear["`*"];
d2 = a - b*p2;Q1 = Maximize[{(p2*(a - b*p2) - (w2*(a - b*p2) - (v2*((a - b*p2))^2)/ 2)), p2 >= a/b - (w2 - c)/(b*v2) && c < w2 < (a - b*c)*v2 + c && a/b > p2 > w2 > 0 && 2/b > v2 > 0}, {p2}]Q2 = Maximize[{(p2*d2 - (w2*d2 - (v2*(d2)^2)/2)), p2 >= a/b - (w2 - c)/(b*v2) && (a - b*c)*v2 + c <= w2 < a/b && 2/b > v2 > 0 && a/b > p2 > w2 > 0}, {p2}]Q3 = Maximize[{(p2* d2 - (((w2)^2 - c^2)/(2*v2) + c*(d2 - (w2 - c)/v2))), p2 <= a/b - (w2 - c)/(b*v2) && 0 < c < w2 < (a - b*c)*v2 + c && 2/b > v2 > 0 && a/b > p2 > w2 > 0}, {p2}]
For Q1, I want to find the optimal p2 to maximize the first expression, i.e., p2*(a - b*p2) - (w2*(a - b*p2) - (v2*((a - b*p2))^2)/ 2)) , the same for Q2 and Q3. In fact, it is easy to get the results for them respectively. However, my final purpose is going to find the global optimality, which means I have to compare the first expressions of the three problems. Therefore, I tried to use command Max[Q1, Q2, Q3], the result is odd. So there are two important questions: Firstly, how to pick up the optimal value of the first expressions from Q1, Q2 and Q3; secondly, which comand can be used to solve this problem of comparison since "Max" doesn't work at all. Thank you very much in advance.
