=7-8 The mathematical relationships that follow were formulated by an operations research analyst at the Smith–Lawton Chemical Company. Which ones are invalid for use in an LP problem, and why?

Maximize profit subject to

= + + +

+ + ≤

−

4 3 8 5 2 2 50 4

1 1 2 2 3 1 2 3 1

X X X X X X X X X X X X X X X X X X X X X 2

1 2

2 3 2 3 1 2 3 1 2 6

1 5 6 3 21 19 0 35 17 5 4 3 80

≥

+ + ≥

− =

+ + ≤

− − +

.

.

3 = 5