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IE403.01 Operations Research Applications IIK UNIVERSITY Midterm Exam 6 Dec 2011 Student Name:...

questions is in the attachment this is operation research course (manufacturing systems)

IE403.01 IŞIK UNIVERSITY 6 Dec 2011 Operations Research Applications Midterm Exam Student Name : ____________________________________________________________________1/ 8 There are 7 questions on this exam. You have 2 hours. Use the back of the pages for your answers if  necessary. 1. (8 points)  Write each of the following   as compactly as possible using summation  and indexed notation. Example:  7 ,..., 1 5 1 = = = j b x j i ij   i. min c 1 y 1  + c 2 y 2  + … + c n y n ii. y 11  + y 12  + y 13  + y 14  = s 1   y 21  + y 22  + y 23  + y 24  = s 2   y 31  + y 32  + y 33  + y 34  = s 3   iii. a 11 y 1  + a 12 y 2  + a 13 y 3  + a 14 y 4  = b 1 a 21 y 1  + a 22 y 2  + a 23 y 3  + a 24 y 4  = b 2 a 31 y 1  + a 32 y 2  + a 33 y 3  + a 34 y 4  = b 3 2. (8 points)  Suppose that the decision variables of a mathematical programming  model are x i,j,t  = amount of product  i  produced on manufacturing line  j  during week  t  where  i=1,…,17 (i.e. 17 total products); j=1,…,5 (i.e. 5 total lines) ; t=1,…,7 (i.e. 7 total  weeks). Use summation  and indexed notation  to write mathematical expressions for each of  the following systems of constraints in terms of the above decision variables,  and  specify how many constraints belong to each system. i. Total production on any line in any week should not exceed 200. ii. The total 7-week production for product 5 should not exceed 4,000. iii. At least 100 units of each product should be produced each week.
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IE403.01 IŞIK UNIVERSITY 6 Dec 2011 Operations Research Applications Midterm Exam Student Name : ____________________________________________________________________2/ 8
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