Please answer all parts of the following question (you must use Calculus concepts learned and show all work):1. NetSell, a the TV remote control supplier for Lumyn Electronics, has a weekly production cost of q TV remote controls that is given byC(q) = 0.000004q3 - 0.03q2 + 100q + 75,000where q is in the interval [0, 10,000].The demand function for this product is given byp(q) = -0.005q + 200.Based on this information, find the following:a) The marginal cost for the company.b) The marginal revenue for the company.c) The marginal profit for the company when 2,000 and 7,000 TV remote controls are manufactured.
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.
Please answer all parts of the following question (you must use Calculus concepts learned and show all work):
1. NetSell, a the TV remote control supplier for Lumyn Electronics, has a weekly production cost of q TV remote controls that is given by
C(q) = 0.000004q3 - 0.03q2 + 100q + 75,000
where q is in the interval [0, 10,000].
The demand function for this product is given by
p(q) = -0.005q + 200.
Based on this information, find the following:
a) The marginal cost for the company.
b) The marginal revenue for the company.
c) The marginal profit for the company when 2,000 and 7,000 TV remote controls are manufactured.
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