The points you found are the vertices of the feasible region. I agree with the first three points you got. However, the last point should be (25/11, 35/11). This point is at the of the intersection of the two lines 8x-y = 15 and 3x+y = 10
So the four vertex points are: (1,9) (1,7) (3,9) (25/11, 35/11)
Plug each of those points, one at a time, into the objective function z = 7x+2y. The goal is to find the largest value of z
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Plug in (x,y) = (1,9) z = 7x+2y z = 7(1)+2(9) z = 7+18 z = 25 We'll use this value later. So let's call it A. Let A = 25
Plug in (x,y) = (1,7) z = 7x+2y z = 7(1)+2(7) z = 7+14 z = 21 Call this value B = 21 so we can refer to it later
Plug in (x,y) = (3,9) z = 7x+2y z = 7(3)+2(9) z = 21+18 z = 39 Let C = 39 so we can use it later
Finally, plug in (x,y) = (25/11, 35/11) z = 7x+2y z = 7(25/11)+2(35/11) z = 175/11 + 70/11 z = 245/11 z = 22.2727 which is approximate Let D = 22.2727
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In summary, we found A = 25 B = 21 C = 39 D = 22.2727
The value C = 39 is the largest of the four results. This value corresponded to (x,y) = (3,9)
Therefore the max value of z is z = 39 and it happens when (x,y) = (3,9)
By definition, the speed is given by the quotient between the distance traveled and the time it takes to travel that distance. We have then that the expression for speed is as follows v = d / t where d: distance t: time Substituting v = (90feet) / (5s) = 18feets / s answer the average rate of the airplane model, in feet per second was 18feets / s
