Quantitative Business Analysis - Assignment Example

Insert Insert Lecturer’s Insert QUANTITATIVE BUSINESS ANALYSIS Question one (2 marks) In the following transportation model,use the northwest-corner method to find the starting solution. Answer Question 2 JoShop needs to assign four jobs it received to 4 workers. The varying skills of the workers give rise to varying costs for performing the jobs. Table 2 summarizes the cost data of the assignments. The data indicate that worker 1 cannot work on job 3, and worker 3 cannot work on job 4.

Determine the optimal assignment. JOB 1 2 3 4 WORKER Subtract the smallest amount in each row from the each row. J1 J2 J3 J4 W1 30 30 NILL 0 W2 50 20 0 10 W3 60 0 20 NILL W4 50 0 40 50 Subtract the smallest amount in each column from each column. J1 J2 J3 J4 W1 0 30 NILL 0 W2 20 20 0 10 W3 30 0 20 NILL W4 20 0 40 50 Cross the zeros using a single line either in horizontal or vertical so as to use the least number of lines.

The number of lines should be equal to the number of assignment to be allocated. If the number of lines is less than the number of assignments to be made: a) Find the smallest uncovered element X=20. b) Subtract X to every element in the matrix. c) Add back to every element covered by a line. If an element is covered by two lines X is added twice. J1 J2 J3 J4 W1 0 50 NILL 0 W2 20 40 0 10 W3 10 0 0 NILL W4 0 0 20 30 Therefore, Worker 1= Job 4; Costs 20 Worker 2= Job 3; Costs 20 Worker 3= Job 2; Costs 30 Worker 4=Job 1; Costs 70 Total cost 20+20+30+70= 140 Question three (2 marks) The Midwest TV Cable Company is in the process of providing cable service to five new housing development areas.

Figure 1 depicts the potential TV linkages among the five areas. The cable miles are shown on each branch. It is desired to determine the most economical cable network. Midwest TV Cable 4 7 2 3 1 7 3 5 2 6 Answer 2 3 2 1 2 3 2 3 Question four (2 points) Determine the shortest route between node 1 and node 8 in the network of Figure 2 route between node 1 and node 8 in the network of Figure 2.

4 2 1 3 2 1 2 7 6 5 6 2 3 1 5 8 Answer 2 4 2 1 2 3 2 1 1 1 3 2 1 1 4 2 Question five (2 marks) Consider the following problem.

Max Z= 5x1+ 8x2 Subject to x2≤ 6, x1 ≤ 4 3x1+ 2x2­ ≤ 18 x1, x2 ≥ 0 X2 A (0, 9) D(2, 6) G (4, 6) E (0, 6) x2=6 C(4, 3) Feasible region 3x1+2x2=18 x1=4 F(0, 0) D (4, 0) B (6, 0) x1 The optimal solution for the above problem is given by: x1= 2 units x2 = 6 units z= $ 58 If the first constraint is changed from, x2≤ 6 to x2≤ 3 what effect will this have on the optimal solution?

Answer If x2 =3 Units and Z= $58 58=5x1 + 8x2 58= 5x1 +8*3 34= 5x1 Therefore, x1 = 6.9 x2 A (13.35, 0) G (6.9, 3) E (0, 3) X2 = 3 Feasible region 3x1+2x2=26.

7 x1=6.9 F(0, 0) D (6.9, 0) B (8.9, 0) x1 Reference H. Bierman, C. P. Bonnini, and W. H. Hausman. Quantitative Analysis of Business Decisions, Third Edition, Richard D.

Irwin, Inc., 1969. Print.