HW 1 Study Guide

The sensitivity range of C1 (profit per X1, bowls) in the Beaver Creek Pottery example was 25<=C1<=66.67. For whatever reason, it became less profitable to produce bowls, so C1 decreased from US$40 to US$30. Considering that C1 is now US$30, what is the correct statement regarding the current sensitivity range of C1? A. The lower limit decreased B. The upper limit increased C. The lower limit didn't change D. There is no upper limit for C1 now E. None of the above

C. The lower limit didn't change

Consider the following linear programming problem: Max Z = 4X1 + 2X2 s.t. X1 <= 4 X2 <= 4 X1, X2 >= 0 The Z obtained from the best combination of X2 AND x1 IS: A. 4 B. 20 C. 16 D. 25 E. None of the above

E. None of the above

Consider the following linear programming problem: Max Z = $300X1 + $100X2 s.t. 30X1 + 70X2 <= 210 20X1 + 10X2 <= 100 X1, X2 >= 0 What is the maximum Z and the value of X1 and X2 at the optimal solution? A. Z = 1500; X1 = 5; and X2 = 0; B. Z = 300; X1 = 0; and X2 = 3; C. Z = 1250; X1 = 3; and X2 = 3.5; D. Z = 3000; X1 = 10; and X2 = 0; E. None of the above

A. Z = 1500; X1 = 5; and X2 = 0;

Administrators at a university are planning to offer a summer seminar. It costs $6000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $75 per student for the administrators to provide the course materials. If we know that 80 people will attend, what price should be charged per person to break even? a. 15 b. 120 c. 155 d.105 e. none of the above

e. none of the above

Consider the following linear programming problem: Max Z = 5X1 + 12X2 s.t. X1 + X2 >= 25 3X1 + X2 >= 45 5X1 + 7X2 >= 20 7X1 + 13X2 >= 83 X1, X2 >= 0 A. The problem is infeasible B. The problem is unbounded C. There is more than one optimal solution D. (12, 7) is the optimal solution E. None of the above

B. The problem is unbounded

Consider the following linear programming problem: Max Z = $12X1 + $5X2 s.t. 8X1 + 5 X2 <= 40 4X1 + 3X2 >= 12 X1, X2 >= 0 Considering that the values for X1 and X2 that will maximize revenue are respectively X1 = 5 and X2 = 0, what is the amount of slack/surplus associated with the first constraint (8X1 + 5 X2 <= 40) - in the optimal point? A. 0 B. 5 C. 8 D. 12 E. None of the above

A. 0

Which of the following combinations of constraints has no feasible region? A. x1 + x2 >= 15 and x1 - x2 <= 10 B. x1 + x2 >= 5 and x1 >= 10 C. X1 + X2 >= 100 and X1 + X2 <= 50 D. All of the above have a feasible region

C. X1 + X2 >= 100 and X1 + X2 <= 50

For the given objective function which of the following combinations of constraints would produce multiple optimal solutions? Max Z = 6x1 + 10x2 A. x1 + x2 >= 15 and x1 - x2 <= 10 B. 3x1 + 5x2 <= 30 and x1 <= 1 and x2 <= 2 C. x1 <= 10 and x2 <= 20 D. 3x1 + 5x2 >= 15 and x1 + x2 <= 10 E. None of the above

E. None of the above

The Pinewood Furniture Company produces chairs and tables from two resources: labor and wood. The company has 120 hours of labor and 100 board-ft. of wood available each day. Demand for table is limited to 8 per day. Each chair requires 3 hours of labor and 4 board-ft. of wood, whereas a table requires 20 hours of labor and 9 board-ft. of wood. The profit derived from each chair is $100 and from each table is $500. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. The correct linear programming model formulation of this problem is:

Max Z = 100x1 + 500x2 Subject to: 3x1 + 20x2 ≤ 120 4x1 + 9x2 ≤ 100 x2 ≤ 8 x1, x2 ≥ 0