3315 Practice Exam 1 (1)
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San Jacinto Community College *
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Course
3315
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
7
Uploaded by SuperHumanIron7208
FULL NAME:___________________________ UTA ID _____________ IE 3315 Practice Exam 1 4 QUESTIONS 25 POINTS PER QUESTION 100 TOTAL POINTS FOR ANY CREDIT ON ANY PART OF A QUESTION YOU MUST PUT YOUR ANSWER IN THE ANSWER BOX AND SHOW CALCULATIONS AFTER THE BOX EXCEPT FOR QUESTION 1. NO CREDIT WILL BE GIVEN FOR AN ANSWER NOT SHOWING THE WORK REQUIRED TO OBTAIN THAT ANSWER. My signature below indicates that I did not give or receive any assistance on this exam and that the solutions I submitted are wholly my own. ____________________________________________________
1. Circle the single correct answer to each part below. a. (5 points) What kind of algorithm is the simplex method? interior point extreme point gradient sorting b. (5 points) Is the objective function of following problem unbounded on the feasible region? Minimize z = 2x
1 + x
2
s.t. - x
1
+ 4x
2
≤
8 x
1
- 2x
2
³
4 x
1, x
2 ³
0. yes no it cannot be determined c. (5 points) Which of the following types of variables allow you to determine if a linear program is feasible? slack surplus imaginary artificial d. (5 points) How many constraints does the following LP have? Maximize z = - 3x
1 + x
2
s.t. x
1
+ 4x
2
≤
8 x
1
- 2x
2
≤
4 x
1 ³
0 x
2 UR. 2 3 4 5 e. (5 points) In solving the LP of part (b) by the simplex method, how many basic variables would there be in each iteration of the algorithm? 1 2 3 4
2. Solve the following linear programming problem using the simplex method and showing your tableaus after the answer box. Maximize z = - 3x
1 + x
2
s.t. x
1
+ 4x
2
≤
8 x
1
- 2x
2
≤
4 x
1,
x
2
³
0. ANSWER (a) (10 points) Does the problem have feasible points? Circle one. Yes No (b) (5 points) Does the problem have a solution? Circle one. Yes No. (c) (10 points) If you circled YES to (b), then the maximum (x
1
*, x
2
*) = _____________
and the maximum objective function value = _________
. If you circled NO to (b), put NA in the blanks.
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3. Solve the following mixed integer programming problem by branch and bound. You must show your tableaus and branch & bound tree. Maximize z = x
1
+ 4x
2
s.t. x
1
+ 2x
2
≤
3 x
1
, x
2
≥
0 x
2
integer ANSWER (a) (10 points) Does the problem have feasible points? Circle one. Yes No (b) (5 points) Does the problem have a solution? Circle one. Yes No. (c) (10 points) If you circled YES to (c), the maximum (x
1
*, x
2
*) = _____________
and the maximum objective function value = _____________
. If you circled NO to (c), put NA in the blanks.
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4. Two small Texas assembly plants for Zoom automobiles manufacture only the Model S Zoomer and distribute them exclusively to three Texas dealers. Sales forecasts indicate that the 2023 Zoomer Model S demand for dealer 1, dealer 2, and dealer 3 will be 270, 450, and 360 cars, respectively, for the model year 2023. The yearly production capacities are 450 and 900 Model S Zoomers at Plants 1 and 2, respectively, for the model year 2023. The model year 2023 transportation cost of shipping a single Model S Zoomer from a plant to a dealer is given below in dollars. Formulate an appropriate optimization problem to minimize the total model year 2023 transportation cost for the above plants and dealers subject to the above production and demand restrictions. Let x
ij
be the number of Model S Zoomers produced at plant i and sent to dealer j. DO NOT SOLVE. Put your formulated problem in the box below. Dealer 1 2 3 Plant 1 160 140 80 Plant 2 50 90 120 ANSWER Minimize z = s.t.