given numbers $0\le a,b,c,d\le1,a+b+c+d=1$. Find numbers $0\le\alpha,\beta,\gamma,\delta\le1$ with sum equaled to $1$, such that expression $(a-d)(\beta-\gamma)+b(-\alpha+\gamma+\delta)+c(\alpha-\beta-\delta)$ is maximal.
Is there any "easy" way to solve this? Thx.
The maximum can't be in the interior since the objective function is linear in the variables. Which boundary point maximizes it depends on $a$, $b$, $c$, $d$. For instance, for $c=1$ the maximum is at $\alpha=1$; for $a=1$ the maximum is at $\beta=1$; for $d=1$ the maximum is at $\gamma=1$; and for $b=1$ any point with $\gamma+\delta=1$ is a maximum.