Samuel is working on a linear programming question. His goal is to sell a certain number of small copiers and large copiers to maximize profit. He has already graphed the feasible region and found the points of intersection listed below as his possible combinations. Let x represents the number of small copiers and y represents the number of large copiers. (1025, 825) (700, 1050) (900, 925) (975, 875) If 758x + 1012y = P is the equation that calculates his profit (P) , which combination of small and large copiers will provide Samuel with the greatest profit?
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.
The question is in the screenshot and the answers are listed below:
A. 700 small copiers and 1,050 large copiers.
B. 1,025 small copiers and 825 large copiers.
C. 975 small copiers and 875 large copiers.
D. 900 small copiers and 925 large copiers.
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