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3 years ago

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Please Help ASAP! Will name Brainliest! Question: Minimize the objective function P = 5x + 8y for the given constraints. x ≥ 0 y

≥ 0 2x + 3y ≥ 15 3x + 2y ≥ 15 Answer: 25, 46, 39, 37.5

1 answer:

maksim [4K]3 years ago

3 0

Answer:

Option D.

Step-by-step explanation:

Minimize the objective function P = 5x + 8y for the given constraints.

$x\geq 0,y\geq 0$

$2x+3y\geq 15$

$3x+2y\geq 15$

The related equations of above inequalities are

$2x+3y=15$

$3x+2y=15$

For $2x+3y=15$ ,

x y

0 5

7.5 0

Plot (0,5) and (7.5,0) and join them by straight line.

For $3x+2y=15$ ,

x y

0 7.5

5 0

Plot (0,7.5) and (5,0) and join them by straight line.

Check the inequalities for (0,0).

$2(0)+3(0)\geq 15\Rightarrow 0\geq 15$ False

$3(0)+2(0)\geq 15\Rightarrow 0\geq 15$ False

It means both lines are solid lines and shaded region for each lies opposite side of (0,0).

From the below graph it is clear that the vertices of feasible region are (0,7.5), (3,3), (7.5,0).

Point P = 5x + 8y

(0,7.5) P=5(0)+8(7.5)=60

(3,3) P=5(3)+8(3)=15+24=39

(7.5,0) P=5(7.5)+8(0)=37.5 (Minimum)

So, minimum value is 37.5.

Therefore, the correct option is D.

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Firdavs [7]

Answer:

$0.0239\frac{in^{3}}{min}$

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)

This diagram will help us visualize the problem better.

So we start by determining what data we already know:

Height=6in

Diameter=3.8in

Radius = 1.9 in (because the radius is half the length of the diameter)

The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:

$r'=\frac{1/1000in}{3min}$

which yields:

$r'=\frac{1}{3000}\frac{in}{min}$

with this information we can start solving the problem.

First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:

$V=\pi r^{2}h$

where V is the volumen, r is the radius, h is the height and π is a mathematical constant equal approximately to 3.1416.

Now, the height of the cylinder will not change at any time during the reborning, so we can directly substitute the provided height, so we get:

$V=\pi r^{2}(6)$

or

$V=6 \pi r^{2}$

We can now take the derivative to this formula so we get:

$\frac{dV}{dt}=2(6)\pi r \frac{dr}{dt}$

Which simplifies to:

$\frac{dV}{dt}=12\pi r \frac{dr}{dt}$

We can now substitute the data provided by the problem to get:

$\frac{dV}{dt}=12\pi (1.9) (\frac{1}{3000})$

which yields:

$\frac{dV}{dt}=0.0239\frac{in^{3}}{min}$

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3 years ago

The table below shows the distance d(t) in feet that an object travels in t seconds: t (seconds) d(t) (feet) 2 64 4 256 6 576 8

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Answer:

128 ft/s; it represents the average speed of the object between 2 seconds and 6 seconds

Step-by-step explanation:

The average rate of change is another way to say slope.

slope = (y2-y1)/(x2-x1)

= (576-64)/(6-2)

= (512/4)

=128 ft/s

This represents the change in ft per second, or the average speed the object is going during the time period.

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3 years ago

Read 2 more answers

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sp2606 [1]

Answer:

a)59.125, b)67.5, c)None

Step-by-step explanation:

Mean = All values added up and divided by the number of values
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Median = Put all numbers in order from least to most and use the middle one, if there are two, use the mean of those two
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2 years ago

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miv72 [106K]

Answer:

4

Step-by-step explanation:

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AB = $\sqrt{((\frac{\sqrt{6} }{2})^2 }$ + $\{(\frac{\sqrt{58} }{2})^2 }$

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= $\sqrt{\frac{64}{4} }$

= $\sqrt{16}$

= 4

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Dominik [7]

The probability is 0.8997.

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With our information, we have
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