Demand function- check solution

[RichaS]

Suppose u(x; y; z;w) = xy + wz. Find the demand func-
tion for x.

Answer: maximum when x=y and w=z
             
Demand: x=m/px+py and y= m/px+py    if px+py<pw+pz
               w=m/pw+pz and z=m/pw+pz   if px+py>pw+pz
               anywhere on the budget line       if px+py=pw+pz

[Abhitesh]

I would think like this.
If prices are such that when consumer spends entire income on x&y 'or' on w&z ;xy>wz. Then the consumer should spend entire income on x&y otherwise on w&z. The corresponding utility will be U=xy 'or' U=wz resp. And we have to maximize this utility.

There will also be a case where xy=wz.

PS - From where do you find these questions.

[RichaS]

Thanks! And Assignments provided by our teacher.