Then evaluate yz+xz in terms of z.
You get a quadratic in z, with the co-efficient of the square being negative.
Hence the quadratic in z is an inverted U-shape.
The derivative of the quadratic being zero (horizontal tangent resting on top of the curve) locates z giving max yz+xz.
Evaluate this and differentiate (then set derivative to zero) to find z that gives the maximum yz+xz.
Substitute in this value of z to find the maximum value of yz+xz.