The vertices of a feasible region are A(1,2), B(5,2), C(1,4). Write a function that satisfies each equation.
a) A is the maximum and B is the minimum.
b) C is the maximum and B is the minimum.
c) B is the maximum and A is the minimum.
To write a function that satisfies each equation, we need to define the objective function and the constraints.
First, let's define the objective function:
The objective function is the equation that we want to maximize or minimize. In this case, we need to define the equation that represents each condition (a), (b), and (c).
Now, let's go through each condition and write the function that satisfies it:
a) A is the maximum and B is the minimum:
In this case, we want to maximize the value of A and minimize the value of B. Since the x-coordinate is the same for A and B, we need to focus on the y-coordinate. Therefore, the objective function for this condition would be:
f(x) = -y
b) C is the maximum and B is the minimum:
In this case, we want to maximize the value of C and minimize the value of B. Again, we focus on the y-coordinate since the x-coordinate is the same for C and B. So, the objective function for this condition would be:
f(x) = -y
c) B is the maximum and A is the minimum:
In this case, we want to maximize the value of B and minimize the value of A. Since the y-coordinate is the same for A and B, we need to focus on the x-coordinate. Therefore, the objective function for this condition would be:
f(x) = x
Note: These objective functions are simplified and assume that the values of A, B, and C are given as input to the function.
To summarize, here are the functions that satisfy each equation:
a) f(x) = -y
b) f(x) = -y
c) f(x) = x
You can plug in the values of A, B, and C into these objective functions to determine the maximum and minimum values for each condition.