Assume that the demand for tuna in a small coastal town is given by 600,000 g1.5 where q is the number of pounds of tuna that can be sold in a month at p dollars per pound. (a) What is the monthly revenue as a function of the demand for tuna? R(q)= (b) Assume that the town's fishery wishes to sell at least 5,000 pounds of tuna per month. This means you are studying the revenue function on the domain [5000,00). Does the monthly revenue function have any stationary points? No Does the monthly revenue function have any singular points? No Use the First Derivative Test to determine if the monthly revenue is increasing or decreasing on the domain [5000,00). The monthly revenue is decreasing v on the domain [5000,00). (c) From your analysis above, how much tuna should the fishery sell per month in order to maximize monthly revenue? q = Ib How much should they charge for tuna in order to sell that much fish? (Round your answer to the nearest cent.) p = dollars per Ib What will be its resulting maximum monthly revenue? (Round your answer to the nearest dollar.) per month
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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