T and half of second is 10

Call them x and y, x>0, y>0, x and y real.

Sum of the first and half the second is 10, so x + 0.5y = 10

We aim to maximise xy given this constraint.

See that y = 20-2x, so xy = 20x-2x^2. The curve of -2x^2 + 20x has a maximum of 50 at x=5, so let's go with that. Then x+0.5y=10, so y=10.

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