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katrin2010 [14]
3 years ago
5

The cost of producing x units of a product is C dollars, where C is given by the function C = 0.25x2 - 80x + 30000. (See the gra

ph provided.) How many units should be produced to generate the lowest cost?
Mathematics
1 answer:
Nat2105 [25]3 years ago
4 0
From calculus, to determine the maxima or minima of the graph, get the derivative of the equation and equate to zero. So, we derive first the equation of the graph and equate to zero.

C = 0.25x² - 80x + 30000
dC/dx = 0 = 0.5x - 80 + 0
0.5x = 80
x = 80/0.5
x = 160 units

The minimum cost (although not asked) is:

C = 0.25(160)² - 80(160) + 30000
C = $23,600

The answer is 160 units.
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The lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

<h3>What is a confidence interval?</h3>

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

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A survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

Sample proportion = p = 378/504 = 0.75

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\rm SD = \sqrt{\dfrac{pq}{n}}

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