introduction to operations research

Contactgear Sdn. Bhd. has branches located in Selangor, Pahang and Johor. They manufacture shelving racks for consumer use. Currently, there are 30 racks stored in Selangor, 40 in Pahang and 30 in Johor. Contactgear has just received orders of 20, 20, 25 and 35 racks from Lam, Ran, San and Zen, respectively. Contactgear has solved their problem using the Transportation Simplex Method. The following is the optimal tableau that they have obtained VI = 7 12 = 10 V3 = 14 V4 = 8 Lam Ran San Zen Supply 7 10 14 8 Selangor 10 20 30 41 = 0 0 0 7 11 12 6 Pahang 5 35 40 U2 = -2 -2 -3 5 15 9 Johor 20 10 30 43 = -2 -3 -3 Demand 20 20 25 35 100 (a) State the optimal delivery plan and cost. (b) Contactgear must change couriers for the Selangor - San delivery (refer c13) but they do not want to recalculate their delivery plan from scratch as this would incur extra costs. By performing Sensitivity Analysis, identify the range of optimality for c13 for which the current basis remains optimal