Question 1206298
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        This minimax problem is very special.

        It is special,  because it can be easily solved  MENTALLY,  based on common sense  ONLY, 

        without using heavy artillery technique of linear programming.



<pre>
Indeed, after reading the post, it should be clear that the winning strategy 
is the most aggressive strategy making SO MANY small boxes as possible,
until the restrictions allow do it; and when the restriction on small boxes
is reached, then to switch making large boxes, until the restrictions on 
large boxes is reached.


It is so, because the profit of each small box is greater than the profit of each
large box (R42 against R14), while each small box requires less amount of 
material than each large box (0.8 sq. m against 1.4 sq. m).


So, it is OBVIOUS that to produce small boxes is more profitable.


The other restrictions (total wood and total working time) do not give a preference to any 
sort of production, and the limitation on the numbers of small boxes and large boxes (like
the warehouse space limitation and the demand) are in favor of small boxes.


So, following to this idea, as many of small boxes should be produced, making 30 small boxes.
(limited by the demand). 

It will require 0.8*30 = 24 sq.m of wood, leaving 42-24 = 18 sq.m of wood for large boxes
and will require 0.5*30 = 15 hours of labor, leaving 24-15 = 9 hours for large boxes.


Now we determine the number of large boxes.  The limitations are

    18/1.4 = 12.86 for wood;

    9/0.5 = 19 from labor hours;
  
    20 from the warehouse space limitations.


So, for large boxes the number is 12.


The maximum profit is 30*42 + 12*14 = 1428 monetary units.


<U>ANSWER</U>.  The optimal strategy is to make 30 small boxes and 12 large boxes,

         making the maximum possible profit of R1428.
</pre>

Solved.


From my point of view, this solution is much more educative than applying 
heavy artillery of the linear programming method without necessity.