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A. Develop a distribution pattern that meets availability and demand constraints and minimizes total shipping costs for Shuzworld, utilizing the appropriate decision analysis tool.
Your current distribution pattern should have Shanghai shipping 1300 units to Warehouse 2, Shuzworld H shipping 300 units to Warehouse 1, 200 units to Warehouse 2 and 1800 units to Warehouse 3, and Shuzworld F shipping 2200 units to Warehouse 1. This transportation plan results in an Optimal Transportation Cost of \$13,600.
The updated production plan you outlined for me increases the production of the Shanghai plant from 1300 units to 2800 units. This is a very advantageous change as it results in an improved Transportation Cost
In Shuzworld’s deck shoe case, R1 = 0.84, R2 = 0.91, and R3 = 0.99. Therefore:

Rs = 0.84 x 0.91 x 0.99 = 0.757 or 75.7% (This is the current system reliability.)

The process with the lowest reliability should be backed up, in this case Machine 1 whose reliability only stands at 84%. To calculate the new process reliability the following calculations are required:

Probability of second machine working
Probability of second machine working
Probability of needing second machine
Probability of needing second machine
Probability of first machine working
Probability of first machine working

So in this case (0.84) + ({0.84} x {1 - 0.84}) = 0.84 + (0.84 x 0.16) = 0.84 + 0.13 = 0.97

0.97 is now the reliability for the combined machine 1 and its back up, the new R1

The reliability equation remains R1 x R2 x R3 = Rs

Therefore the new system reliability is Rs1 = 0.97 x 0.91 x 0.99 = 0.873 or 87.3% if you back up machine 1.

If you were to backup machine 2 the same calculation applies, but we solve for R2:
R1 = 0.84, R2 = 0.91, and R3 = 0.99
R2 redundant = (0.91) + ({0.91} x {1 - 0.91}) = 0.91 + (0.91 x 0.09) = 0.91 + 0.08 = 0.99
New system reliability with Machine 2 redundant = Rs2= 0.84 x .99 x 0.99 = 0.823 or 82.3%

If you were to choose to back up