The weekly cost C (in dollars) of running a telemarketing firm is related to the number N of telephone operators. There is a fixed cost of $1400 per week, and each telephone operator costs the firm $200 per week. For example, if there are 10 operators, then the weekly cost is $3400. a) Use a formula to express the weekiy cost Cas a function of N, the number of telephone operators. Make sure to include function notation. Use functional notation to express the weekly cost if 4 telephone operators are b)+ used, and then use your formula from part a to calculate that cost. Make sure to include appropriate units. c) The costs of running the firm have now increased, and the new weekly cost D (in dollars) is given by the formula D = 1500 + 250N, where N is the number of telephone operators. i) ) Solve this new equation for N to get a formula for Nas a function of D. ii) The firm can afford weekly costs up to $3500. Use your formula in part i to determine how many operators the firm can afford to hire.
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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