A particular notebook computer has a price/demand function of p(n) = 1200 – 36n dollars, where n is the number in thousands of computers sold in the market. The manufacturer's fixed cost of operations is 4,400 dollars while the variable cost of production 140 per computer. In the previous notebook computer problem, what is the profitable range of production? O1. Between 5000 and 24444 computers O II. Between 5444 and 24000 computers II. Between 5454 and 24040 computers O V.Between 5000 and 25000 computers In the previous notebook computer problem, at what level of sales does maximum revenue occur? OL. 16667 computers O II. 16000 computers O II. 17000 computers O V. 16335 computers In the previous notebook computer problem, at what level of sales does maximum profit occur? O1. 15622 computers O II. 14000 computers O II. 16667 computers O V. 14722 computers
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.
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