Let f(x, y)= xy+5x+4y model the utility a consumer feels based on the number of the number of cups of coffee, x, and the number of donuts, y, consumed on a given thursday. find the absolute maximum and absolute minimum values of f(x, y) over the triangular region with vertices (0,0), (2,0), and (0,2). be sure to include any critical points found on each boundary as well as any critical points inside the region. hint: the equation of the diagonal boundary is y=−x+2.

Normally he uses 100,100,100 grams of coffee for 101,010 cups.

That's  (100,100,100) / (101,010)  =  990.992  grams per cup.

If he wants to use 20% more, that would be  

                     (1.2) x (990.992) = 1,189.19 grams per cup.

To make a pot of 15 cups, he would need to use

                     (15) x (1.2) x (990.992) = 17,837.9 grams,
 
                                                           (about 39.3 pounds of coffee) .


This troubles me.  He normally uses almost 2.2 pounds of coffee 
for every cup, and now he has to cram 39 pounds of coffee into
that little pot.  It seems that Mitchell has a serious caffeine problem,
and plus he's spending a fortune on coffee.  How can this be ?
These numbers just don't make sense !

Could it be that the numbers given in the question are not what they
seem to be ?  Could it be that all those ones and zeros are not really 
decimal numbers, i.e. written in base-ten ?  Could it be that they are
actually binary numbers instead ?  The question doesn't tell us what
base the numbers are written in ... but the results I got from my 
calculations are just so totally weird !   I'll go through the whole thing
again, only this time, I'll assume that the numbers in the question are 
binary numbers ... base-2 ... and see how that works out.

Normally he uses 100100100 grams of coffee.  If that's a binary 
number, then it translates into the decimal number  292 grams.
Ah hah !

He uses that to prepare  101010 cups.  If that's a binary number,
then it translates into  42 cups.

This is looking much better. In fact, I think the coffee has suddenly
become pretty weak !  Lets carry on . . .

NOW, Mitchell normally uses  292 grams for 42 cups.

20% more than that is  (1.2) x (292/42) grams per cup.

To make 15 cups of the new stuff, he'll need

          (15) x (1.2) x (292/42)  =  125.142 grams of coffee

                                                about  4,4 ounces !

                                                    Much better !

I suppose 'Maimom61' expects the answer as a binary number.
I'll need to round the amount of coffee to the nearest whole
number first, because I don't remember how to write decimals 
in binary.

125.142 grams, rounded to the nearest whole gram, is 125 grams.    

As a binary number, that's   1 1 1 1 1 0 1  grams