Equation with 4 variables

Question

What are the maximum numerical values for each variable in:

3x+4y+5z+6w=144

 

So that the equation is true, and no variable is negative.

Answer 1

There are no maxima for individual terms; this just says that the total computed on the left side must equal 144, exactly.  If some variables take on very negative values, then others could take on very positive values.

Answer 2

If any of them can have a negative value then the possibilities are infinite.  so let's say each variable must be at least 0.  To find the maximum value of each variable, set the other three equal to zero and solve the equation.  For example:

 

3x + 4(0) + 5(0) + 6(0) = 144

3x = 144

x = 48

 

For x to be larger than 48, at least one of the other variables would have to be negative, and then x could be as large as we wanted.

I'll let you figure out the other three variables.