Suppose you run a business with a price function p (x) = 50 - 0.03z and Cost function C (2) = 100 + Se Assume that xis measured in 10.000's of items, that pis measured in S. and that Revenue and Profit are measured in $10,000's 1. Find the formula of your company's Revenue and Profit functions. 2. Generate a graph on Desmos.com of your Revenue, Cost, and Profit functions. 3. Use your graph to find the intercepts and turning points of the Revenue function. For the near future, your company just wants to generate cash flow and name recognition. They might accomplish that by maximizing Revenue. In a short paragraph, explain the steps you took to complete all the above tasks, and tell me the price your company should set, how many items you should make and sell, and what your company's revenue will be. Also include a link to your Desmos.com graph. Separately, each student should email me a one-sentence autobiography, explaining how they contributed to the solution.
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.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
