Q&A Hero

Question

What combination of a and b will yield the optimum for this problem?

Maximize $6a + $15b, subject to (1) 4a + 2b < 12 and (2) 5a + 2b < 20 and (3) a, b u2265 0.

A) a = 0, b = 0

B) a = 3, b = 3

C) a = 0, b = 6

D) a = 6, b = 0

E) cannot solve without values for a and b

Answer: C

19) A maximizing linear programming problem has two constraints: 2X + 4Y < 100 and 3X + 10Y < 210, in addition to constraints stating that both X and Y must be nonnegative. The corner points of the feasible region of this problem are

A) (0, 0), (50, 0), (0, 21), and (20, 15)

B) (0, 0), (70, 0), (25, 0), and (15, 20)

C) (20, 15)

D) (0, 0), (0, 100), and (210, 0)

E) none of the above

Answer: A

20) A linear programming problem has two constraints 2X + 4Y u2264 100 and 1X + 8Y u2264 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

A) There are four corner points including (50, 0) and (0, 12.5).

B) The two corner points are (0, 0) and (50, 12.5).

C) The graphical origin (0, 0) is not in the feasible region.

D) The feasible region includes all points that satisfy one constraint, the other, or both.

E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

Answer: A

21) A linear programming problem has two constraints 2X + 4Y u2265 100 and 1X + 8Y u2264 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

A) There are four corner points including (50, 0) and (0, 12.5).

B) The two corner points are (0, 0) and (50, 12.5).

C) The graphical origin (0, 0) is in the feasible region.

D) The feasible region is triangular in shape, bounded by (50, 0), (33-1/3, 8-1/3), and (100, 0).

E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

Answer: D

22) A linear programming problem has two constraints 2X + 4Y = 100 and 1X + 8Y u2264 100, plus non-negativity constraints on X and Y. Which of the following statements about its feasible region is true?

A) The points (100, 0) and (0, 25) both lie outside the feasible region.

B) The two corner points are (33-1/3, 8-1/3) and (50, 0).

C) The graphical origin (0, 0) is not in the feasible region.

D) The feasible region is a straight line segment, not an area.

E) All of the above are true.

Answer: E