# How can I find &#x03BB;<!-- λ --> H </msub> and &#x03BB;<!-- λ -->

How can I find ${\lambda }_{H}$ and ${\lambda }_{T}$ such that

Is this problem equivalent to finding $x$ and $y$ such that
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notemilyu1208
Each of the functions is convex, their max is then convex, so the solution of the maximization lies at one the corners: (0,0), (0,1), (1,0) and (1,1). It should be (0,0).

What is not clear is the $<1$. Is it a constraint? If so it should be written as a constraint.

If you want to impose the value is $<1$ then it is just a matter of increasing the variables from zero until the point you reach 1 or one of them hits one.