What digits? is there specific types?
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)
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Final Answer: 39
Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W = ![2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750](https://tex.z-dn.net/?f=2%20%5Ctimes%20%5Cint%5Climits%5E%7B25%7D_0%20%7B0.6%20%5Ccdot%20x%7D%20%5C%2C%20dx%20%2B%20375%3D%202%20%5Ctimes%20%5Cleft%5B0.6%20%5Ccdot%20%5Cdfrac%7Bx%5E2%7D%7B2%7D%20%5Cright%5D%5E%7B25%7D_0%20%2B%20375%20%3D%20750)
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
![W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5](https://tex.z-dn.net/?f=W_2%20%3D%20%20%5Cint%5Climits%5E%7B25%7D_0%20%7B0.6%20%5Ccdot%20x%7D%20%5C%2C%20dx%20%2B%20375%3D%20%5Cleft%5B0.6%20%5Ccdot%20%5Cdfrac%7Bx%5E2%7D%7B2%7D%20%5Cright%5D%5E%7B25%7D_0%20%2B%20375%20%3D%20562.5)
The work done in pulling half the rope, W₂ = 562.5 lb·ft
Answer:
$0.29
Step-by-step explanation:
Multiply the unit weight ($0.24/ounce) by the weight (1.2 oz.):
$0.24 1.2 oz
.24 * 1.2 = $0.288
So, the rounded answer will be $0.29
Answer:
F(8)=120
Step-by-step explanation:
f(x)=15x
f(8)=15(8)
f(8)=120
