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0H543 '10Maximize 3 X+y for the bounded feasible region dispialed alove:...

Question

0H543 '10Maximize 3 X+y for the bounded feasible region dispialed alove:

0H 5 4 3 ' 10 Maximize 3 X+y for the bounded feasible region dispialed alove:



Answers

Find the values of $x, y, z$ that maximize
$$3 x+5 y+z-x^{2}-y^{2}-z^{2}$$
subject to the constraint $6-x-y-z=0.$

For this problem. The question reads. What are the Vergis ease of the feasible region bounded by the constraints at the right, we have experts. Wise lesson equals a 32 experts wise us and equal to four X is greater than equal to zero. And why is greater than equal to zero? So we're gonna start by graphing all four constraints. We have experts wise. Listen people 23 in the green We have two experts wise as an equal to four in the purple, we have X is greater than equal to zero in the black And then we have why is greater than equal to zero in the red. So our feasibly region is this area right here We're all four constraints overlap and we have to figure out our vergis ese for this feasible region. So our first courtesy is gonna be zero comma zero. Then we have zero comma three and our next Verdecia is gonna be one comment to. And then our last word isi is gonna be two comma zero. So we have zero comma, 00 comma 31 comma two and two comma zero as our Vergis is for the peaceful region. Given these four constraints

According to the ocean we have given values have physical do three x plus fire away. We have the objective function and the work is is theories. It is one comma. Zero b is one go Martin See is seven Goldman six. The is cell in Goma. Nine. We can say that the value off the object function in each were text theories half off a ethical do three in tow one plus five into zero. There is a cool dude three and F B is equal to three in tow. One plus five into 10 days 53 half off. See Gary's three into seven plus five into six is equal to 51 f off D is three into seven plus five into nine is equal to 66. The maximum value off the object function is F maximum from the maximum. The values is three 53 51 66. The maximum value is 66 and the minimum value there is minimum value come from the points. 3 53 51 66 The minimum value is 30 began set minimum value comes from dairies. Three in the point is ban coma zero and duh maximum value. He's 66. Deary's in seven. Coma. Nine

To grant a system of inequalities. We grabbed each inequality first and then we get the common reason, which is a phys bridge. We start by the first. Inequality is greater than or equal zoo and smaller than request line. Because we have on the X you, we can grow these two lines. X equals mine and X equals zero, which they are vertical lines that poses by the X X is in zero and mine The first line, his oil excess and second line is this vertical line We grow It sold lines because we have equal signs here and the area or the region is the area between them. The second inequality X minus Roy is greater than or equal four. We drew the line X minus. Toy equals the first point by putting X's you given, boy equals negative too. And by putting boy zero Ex Equitable, the 1st 0.0 and negative school. The second point is for fans. You we grow a solid line that bus between these two, like two points on we can. This the origin to get the region zero minus zero is greater than four, which is false. This means that we have the area over there to the origin. We have this area here for the second inequality The third inequality three x last five Roy. Smaller than for equals 30. We drew the line three X plus five boy equals 30 We but x equal we booked zero gives y equal six. And by putting boys, you gives X equals. The first point is year zero and sex the second point is here 10 0 Then on do you hear? We grow a solid line. The bus between these two points and we tested the origin the chick their area zero and zero smaller than 30. Which is true. This means that we have this area with a the fourth Inequality boy is greater than equal zero. We have all boosted y values. This means that this mine with us and we have all Muslim. Why values? We have to figure out the coma region the Kama region boys here in this triangle bounded by this solid line this green solid line and the horizontal X X is and the inquiry in Horan's like all these lines are so the lines and we have this founded area or bounded visible region

Here were given a objective function that is defined regime equals four X plus five way we have a series of constraints that will graph with an objective function. And we're going to draft that looks something like this. Let up a little bit remember those red curve, we can go ahead and we can move and I actually see this red curve, this purple curve are parallel. Um So what that means, we put them on top of each other if we shift them appropriately, so we're gonna go ahead and what kind of want to do that? Yeah. Um So if we go ahead and we should the current type of purple curve, you know, we're going to have something like this, right? I'll be the new writer curve there. Um Now this region here becomes unbounded, right? So we're looking, you know anything really I think of beyond those quadrants, right? Anything really here. So what is our minimum occur? Well, I mean, I'm still abounded as can occur at the 0.53 Which is up here, Right this point right here, drink blue stand out better. This is our minimum point. Well, it's not really gonna be a maximum point. So what we can say now, our minimum is that five comma three. So z here we have four times five is 20 plus 15 gives us 35 and there's no max region is unbounded. And that's your solution for this question.


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