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3 years ago

Solve the following linear programming problem.

Mathematics

1 answer:

Reil [10]3 years ago

8 0

Find the intersection point between the 2 restraint equations:

30 - 2x = 12 - \frac{1}{2} x \\ \frac{3}{2} x = 18 \\ x = 12

Substitute back in to find y-value:

y = 30 - 2(12) = 6

P is maximized at point (12,6)

P = 9(12)+9(6) = 162

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Rudik [331]

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The ratio of their volumes is: $\frac{729}{64}$

Step-by-step explanation:

If the cones are similar, then the ratio of their heights should equal the ratio of their radiuses. If we call R the radius of the larger cone (the one of height 9 cm) and r the radius of the smaller cone (the one of height 4 cm), then the following proportion should be verified:

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Now we input this information in the formula for the volume (V) of the largest cone, and for the volume (v) of the smaller cone, recalling that the volume of a cone is the product of the area of the cone's circular base ( $\pi *\,radius^2$ ).

$v=\frac{\pi\,r^2\,4\,}{3} =\pi r^2\,\frac{4}{3} \\V=\frac{\pi\,R^2\,9}{3}=\frac{\pi\,(\frac{9\,r}{4} )^2\,9}{3}=\frac{\pi\,r^2\,729}{16*3}=\pi r^2\,\frac{243}{16}$

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