inequalities: find min value of z=18x+12y, subject to constraints

[jadien]

hi guys,

I have this maths problem i have literally been working for hours on and cant seem to get it right. I haven't done math since i graduated 4 years ago, so i am extremely rusty...

here's my problem:
given the inequalities
2x+6y which is greater than and equal to 30
4x+2y which is greater and equal to 20
y which is greater and equal to 2
xy which is greater than and equal to 0

determine the minimum value of the function z=18x+12y subject to the set of inequalities.

i have drawn the graph already, this function thing is what i cant seem to wrap my head around.

any help would be appreciated

 

[stapel]

I haven't done math since i graduated 4 years ago, so i am extremely rusty...

It's okay. You can work with whatever they covered in class, during the review or whatever at the beginning. (This, by the way, is why you took a placement test: so you'd be placed in the course best suited to how much you do remember from all those years ago.)

given the inequalities
2x+6y > 30
4x+2y > 20
y > 2
xy > 0

Is the last one really a product, "xy", meaning "x times y", or was perhaps a comma omitted, so this is really the standard constraint of "each of x and y is non-negative"?

determine the minimum value of the function z=18x+12y subject to the set of inequalities.

i have drawn the graph already, this function thing is what i cant seem to wrap my head around.

You've done the hard part: doing the graphing of the various inequalities to determine the feasibility region, followed, of course, by finding the coordinates of the corner points of that region.

Now, plug those corner points (that is, their x- and y-values) into the optimization function. Simplify to obtain the corresponding values of z. Then pick the corner point that gives the lowest value of z. This is the "optimal" solution of the system of inequalities, and the corresponding lowest z-value is the value for which they've asked you.