The dimension of the container of this size that has the minimum cost is , and
The given parameters are:
- Volume = 480m^3
- Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.
Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
Substitute 480 for V
And the objective cost function would be:
Differentiate the cost function using Lagrange multipliers
Divide equation (1) by (2)
Factor out 2
Cross multiply
Evaluate the like terms
Divide both sides by 3z
Divide the first equation by the third
Factor out 2
Cross multiply
Cancel out the common terms
Divide both sides by y
Make z the subject
So, we have:
and
Recall that:
Substitute and
So, we have:
Multiply both sides by 3/4
Take the cube roots of both sides
Recall that:
So, we have:
Also, we have:
So, we have:
Hence, the dimension of the container of this size that has the minimum cost is , and
Read more about Lagrange multipliers at:
brainly.com/question/4609414
Answer:
The correct answer is 9 inches : )
Step-by-step explanation:
I took the test and got it right
Answer:
So, I know that we will have to find the Area of the "Shape" And I see a *Unlabeled/Unknown* Shape that we have to find the answer of/to.
Step-by-step explanation:
To find the volume, you multiply length times width times height, which is 3x1x2, which equals six. So the volume of the fish tank is 6 cubic feet. Volume is also how loud a sound is.
To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
Maybe the Definitions Can help, Have a nice day
Answer:
The middle 90% of all freshman biology majors' GPAs lie between 2.31 and 3.43.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 2.87 and standard deviation .34.
This means that
Middle 90% of scores:
Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile.
5th percentile:
X when Z has a pvalue of 0.05. So X when Z = -1.645.
95th percentile:
X when Z has a pvalue of 0.95. So X when Z = 1.645.
The middle 90% of all freshman biology majors' GPAs lie between 2.31 and 3.43.
Answer:
120°
Step-by-step explanation: