Question 1181641
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The AI solution from the other tutor is correct.<br>
In that solution, the steps outlined say that you need to evaluate the objective function at each corner of the feasibility region.  And that is what most references say.<br>
However, in fact it is NOT necessary to evaluate the objective function at every corner of the feasibility region.<br>
The corner of the feasibility region where the objective function is maximized can be determined from the slopes of the constraint boundary lines and of the objective function.  The idea there is that the objective function will be maximized where a line with the slope of the objective function just touches the feasibility region.<br>
In this problem, the constraint boundary line equations are x+y=4000 (slope -1) and 2x+3y=9000 (slope -2/3); the objective function is P=25x+30y (slope -5/6).  Since -5/6 is between -1 and -2/3, the objective function is maximized at the intersection of the two constraint boundary lines.<br>
{{{x+y=4000}}}
{{{2x+3y=9000}}}
{{{2x+2y=8000}}}
{{{y=1000}}}
{{{x=3000}}}<br>
ANSWER: Profit is maximized when 3000 barrels of type A and 1000 barrels of type B are refined each week.<br>