The cost function C(x) = 15,000 + 70x + 1,000/x gives the cost in dollars to produce x units of a commodity. a. Find the marginal cost when the production level is x = 100 units. When they produce 100 units, the marginal costs is ----------Select Units---------- dollars per dollar per unit dollars per unit units dollars In other words, the approximate cost to produce the 101st unit is dollars. b. Find the average cost per unit when they produce 100 units. When they produce 100 units, the average cost per unit is dollars. c. Fill in the blanks: Since the marginal cost is ----------Select Units---------- greater than less than equal to the average cost per unit, increasing production from 100 units will cause the average cost per unit to ----------Select Units---------- increase. decrease.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
The cost function
gives the cost in dollars to produce x units of a commodity.
a. Find the marginal cost when the production level is x = 100 units.
When they produce 100 units, the marginal costs is ----------Select Units---------- dollars per dollar per unit dollars per unit units dollars
In other words, the approximate cost to produce the 101st unit is dollars.
b. Find the average cost per unit when they produce 100 units.
When they produce 100 units, the average cost per unit is dollars.
c. Fill in the blanks: Since the marginal cost is ----------Select Units---------- greater than less than equal to the average cost per unit, increasing production from 100 units will cause the average cost per unit to ----------Select Units---------- increase. decrease.
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