Question 1050643
<pre><b>
Since we are trying to make AB large as possible, 
we first see if A can be 8.  So let's see what
happens when we assume A = 8.

   {{{81 <= AB <= 86}}}

But 

{{{23000 <= AB*CDE <= 25000}}}

{{{23000/CDE <= AB <= 25000/CDE}}}

Then {{{23000/CDE>=81}}} and {{{25000/CDE<=86}}}
     {{{23000>=81*CDE}}} and {{{25000<=86*CDE}}}
     {{{"283.9...">=CDE}}} and {{{"290.6..."<=CDE}}}

That's not possible.  

So A cannot be 8.

So we try A=6
    
We see if it is possible to make AB as large as possible
by making B=8

Then {{{68*CDE >= 23000}}}
     {{{CDE >= "338.2..."}}}

We can do that only by making CDE = 341

Answer:  {{{68*341 = 23188}}}, so the largest possible 
         value for AB is 68.

Edwin</pre></b>