Engineering estimates show that the vanable cost of manutactunng a new product wil be $31 per unit Based on market research, the selling price of the product is to te $139 per unit and variable selling expense is expected to be $14 per unit The fixed costs applicable to the new product are estimated to be $2660 per penod and capacity is 135 units per penod Find algebraic statements for the following (a) the revenue function (b) the cost function (a) Write an algebraic expression for the revenue function. Total Revenue= (Type an expression using x as the variable. Do not include the $ symbol in your answer) (b) Write an algebraic expression for the cost function Total Cost= (Type an expresSion using xas the variable Do not include the $ symbol in your answer)
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.
Step by step
Solved in 2 steps
