Question

I have two problemson polygonal convex sets which I do not understand.

The first: Find the minimum value of f(x,y) = 2x-y+2 for the polygonal convex set determined by this system of inequalities:

x is more than or equal to 1
x is less than or equal to 3
y is more than or equal to 0
1/2x + y is less than or equal to 5

The second problem:

This system forms a polygonal convex set: x is less than or equal to 0;
y is more than or equal to -x, if x is between 0 and -6.

y is less than or equal to 10; 2x + 3y is more than or equal to 6, if x is between -12 and -6.

What is the area of the closed figure?


I do not have a clue as to how to do either of these problems.

Answer 1

I don't know what a 'polygonal' or a 'convex' set means. Your four inequalities define a trapezoidal region of x,y space. You can easily plot it on a graph. The lowest value of 2x - y + 2 in that space occurs where x is least (1) and y is highest (4.5). At that corner of the trapezoid,
2x-y+2 = 2 - 9 + 2 = -5

If that is what is meant by your problem, you should be able to answer the second question by a similar procedure