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Click right here to watch ALL difficulties on Linear-equationsInquiry 665012: A manufacturing facility deserve to develop 2 commodities, x and y, through a profit approximated by P = 14x + 22y � 900. The production of y have the right to exceed x by no even more than 200 devices. In addition, production levels are limited by the formula x + 2y ≤ 1600. What manufacturing levels yield maximum profit? A. x = 400; y = 600B. x = 0; y = 0C. x = 1,600; y = 0D. x = 0; y = 200 Answer by KMST(5293) (Sjust how Source): You deserve to put this solution on YOUR website! Obvious constraints are: and (no negative production)Given constraints are:( cannot exceed by even more than ,the difference has to be or less),and also. Since of those constraints,there is a feasibility area.You just have the right to work-related in that area of the x-y plane.That region is bordered by the lines stood for by , , , and .You deserve to graph the lines. graphs as the red slanted line ,and graphs as the green line.Your feasibility area is tue quadrilateral through components of the x-axis, the y-axis and also the green and also red lines for sides.You have the right to uncover the intersection points for each pair of lines.For instance, resolving gives you the solution through for point (400,600), where the red and green slanted lines intersect.

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The vertices of your feasibility region are:(0,0) , (0,200) , (400,600) and (1600,0).The maximum for will occur at 1 of those points.(In some cases it could occur at 2 of vertices and the totality segment connecting them).All you need to do is calculate for each of those 4 points.I will show you the calculation for 2 of them:For point (400,600), through and ,.For allude (1600,0), .The various other points provide you smaller sized values for ,so the solution is point (1600,0),through and . THE REASON WHY IT WORKS THAT WAY:The function to maximize, is a duty of x and y,which can be represented in 3 dimensions,wit being the 3rd, dependent variable.As with altitude as a function of 2-dimensional works with (latitude and longitude),we can reexisting the function on paper by making a contour map.The contour lines would certainly be .Luckily for us, the feature is linear in and ,so those contour lines will certainly be straight lines, favor the blue line listed below.The blue line is the graph of That is the line for .As you change the constant, the line alters,but all the various other contour lines are parallel to that blue line.As rise the value for the consistent the lines moves away from the origin, till it moves out of your feasibility region.You want the values (for , and for the largest possible ,when you reach the finish of the feasibility region.In general, that will certainly happen at one of the vertices, or at 2 of the vertices and the side that joins them.In this case it happens at suggest (1600,0).The maximum for P will be found at (1600,0)where