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inysia [295]
3 years ago
5

What is the maximum value of P = 24x + 30y, given the constraints on x and y listed below? x+y (less than or equal to) 5 x-y (gr

eater than or equal to) -1 x (greater than or equal to) 0 y (greater than or equal to) 0 120 132 138 150
Mathematics
1 answer:
valentina_108 [34]3 years ago
6 0

Answer:

Step-by-step explanation:

We have to first find the vertices of the feasible region before we can determine the max value of P(x, y). We will graph all 4 of those inequalities in a coordinate plane and when we do that we find that the region of feasibility is bordered by the vertices (0, 0), (0, 1), (2, 3), and (5, 0). Filling each x and y value into our function will give us the max value of that function.

Obviously, when we sub in (0, 0). we get that P(x, y) = 0.

When we sub in (0, 1) we get 24(0) + 30(1) = 30.

When we sub in (2, 3) we get 24(2) + 30(3) = 138.

When we sub in (5, 0) we get 24(5) + 30(0) = 120.

Obviously, the vertex of (2, 3) maximized our function for a value of 138.

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Answer:

x>-6

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Step-by-step explanation:

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Use them to compute the slope:
m = (1 - 10) / (9 - 1)
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Then set up the "point-slope form":
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You choose some point (x0, y0) that the line crosses through. We already know the line passes through (1,10) pretty well, so let's use that.

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The above equation will work fine for an answer, but let's go a step further and solve for y.

y - 10 = -9/8x + 9/8
y = -9/8x + 9/8 + 10
y = -9/8x + 9/8 + 80/8
y = -9/8x + (9 + 80)/8
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