Question 1199522
<br>
{{{a+1/((c+1)/b)}}} = {{{a+b/(c+1)}}} = {{{(a(c+1)+b)/(c+1)}}} = {{{(ac+a+b)/(c+1)}}}<br>
{{{(ac+a+b)/(c+1)=32/9}}}<br>
Certainly if we are wanting the product abc to be minimum, we want c to be as small as possible; so try c=8.<br>
{{{(8a+a+b)/9=32/9}}}
{{{9a+b=32}}}<br>
Again we want the product abc to be minimum; that means the product ab should be minimum.  The minimum value of the product ab, subject to the constraint 9a+b=32, is when a=3 and b=5.<br>
ANSWER: abc = 3*5*8 = 120<br>