Question 1185780
.


The analysis in the post by @CPhill is either incomplete or incorrect.


Below I explain WHY it is so.


<pre>
If to accept interpretation of the problem as in the post by @CPhill,  
then the problem is


    maximize 12800x + 8400y  under these constraints

    6x + 7y <= 42

    4x + 3y >= 48

    x >= 0,  y >= 0.


But the feasibility domain under these constraints is  {{{highlight(highlight(EMPTY))}}}.


Indeed, it is obvious that in positive domain for x and y

    4x + 3y < 6x + 7y.


So, if (x0,y0) is the point in the feasibility domain, then 

    48 <= 4x0 + 3y0 < 6x0 + 7y0 <= 42,


and we arrive to the absurdist inequality  48 < 42.


This contradiction disproves the existence of solutions.


So, the answer for this analysis is that the given problem HAS NO solution.
</pre>

<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;There is EMPTINESS at this point.</H3>