A fast-food restaurant determines the cost and revenue models for its hamburgers. C= 05.x+7100, 0 ≤ x ≤ 50,000 R= 1/10,000(67,000x - x^2), 0 ≤ x ≤ 50,000 (a) Write the profit function for this situation. P = ? (b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answer using interval notation.) (c) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit. Number of hanburgers? Pick one of the reasons below to dertemine your reasoning. a)Because the function changes from increasing to decreasing at this value of x, the maximum profit occurs at this value. b)The restaurant makes the same amount of money no matter how many hamburgers are sold. c)Because the function changes from decreasing to increasing at this value of x, the maximum profit occurs at this value. d)Because the function is always increasing, the maximum profit occurs at this value of x. e)Because the function is always decreasing, the maximum profit occurs at this value of x.
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.
A fast-food restaurant determines the cost and revenue models for its hamburgers.
(b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answer using interval notation.)
(c) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit.
Pick one of the reasons below to dertemine your reasoning.
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