9514 1404 393
Answer:
Explanation:
The signs on x and y tell you that C will be maximized when x is smallest and y is largest. C will be minimized when the reverse is true.
Maximum C: x = -2, y = 2.
C = -2(-2) +3(2) = 10 . . . max
Minimum C: x = 4, y = -2.
C = -2(4) +3(-2) = -14 . . . min
_____
Comment on signs
When the sign is negative, as for -2x, it means the value will go down when x goes up, and vice versa. So, the maximum value of this term will found where x has its minimum value.
When the sign is positive, as for 3y, the value of the term will increase when y increases. So, the maximum value of this term will be found where y has its maximum value.
__
The attachment shows a graphical interpretation of the question. The corners of the "feasible solution space" are the combinations of x- and y- that need to be examined. Once you know the slope of the "objective function" (C) is positive, you know the only corners of interest are the ones on upper left and lower right.