This is the models from cost and revenue that I found already. Model for Cost: C(x)=50.8x+73.4 Model for Revenue: R(x)=-0.956x2+157x+0 This is the help that I need: Enter the value of a. <--- -0.956 Enter the value of b. Enter the value of c. Use your profit model P ( x ) to compute P ( 45 ), rounded to the nearest tenth.
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.
Recall that profit can be computed in terms of revenue and cost. Assume that the annual widget sales match the annual widget demand and annual widget production. Construct a model for profit using the models for revenue and cost that you found in the Revenue and Cost sections.
Find the model for profit P ( x ), where P ( x ) is the total annual profit in dollars for x widgets sold, and write it as P ( x ) = a x 2 + b x + c.
Note: You are using the fact that P ( x ) = R ( x ) − C ( x ), not creating a table of data.
This is the models from cost and revenue that I found already.
Model for Cost: C(x)=50.8x+73.4
Model for Revenue: R(x)=-0.956x2+157x+0
This is the help that I need:
- Enter the value of a. <--- -0.956
- Enter the value of b.
- Enter the value of c.
- Use your profit model P ( x ) to compute P ( 45 ), rounded to the nearest tenth.
- There are two x values such that P ( x ) = 0. Find the larger one, rounded to the nearest whole number.
- There are two x values such that P ( x ) = 0. Find the smaller one, rounded to the nearest whole number.
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