MATHEMATICS II

Hence the solution is the point (-1,2)

(it does not satisfy the second inequality)

(it does not satisfy the second inequality)

(it does not satisfy the second inequality)

(it satisfies both of the inequalities)

(it does not satisfy the first inequality)

except the choice C. The system of equations corresponding to the system given in C

has the intersection point at 

Hence the minimum value of given constraint set is -15

When we add them we get 3y=9 and y=3. For y=3 by the first equation we get x+6=4 that gives x=-2. Hence the corner point is (-2,3)

we get a corner point (-3,1). In addition considering all constraints (especially x≤0, y≥0) we see that 

are other corner points of the constraint set. Secondly, we will find the values of these corner points under the goal function:

The maximum value is 3/4.

Thus, the maximum value is 82

is the point (4,3). Considering the other constraints we obtain that

are other corner points. Thus, (0,4) is not a corner point of constraint set.

The correct answer is A

The correct answer is D.

The maximum value is 30.
The correct answer is E.

The correct answer is B.

The corner points are:

The values of f at these points are : 0, 36, 39, 35. The greatest  value is 39.
The correct answer is C.

we have

The corner points are: (0,0), (0,5), (2,5), (7,0). The maximum is attained at the point (2,5) and equals

The correct answer is B.

The correct answer is A.

From the second equation 

The correct answer is E.

The maximum value of the goal function at these points is attained at the point

This value is 23.
The correct answer is D.