gamma industries manufactures its own products at its 3 factories. it then delivers these products to its 3 stores. each of the 3 stores orders a different amount of the product from the factories, an

Project Description:

gamma industries manufactures its own products at its 3 factories. it then delivers these products to its 3 stores. each of the 3 stores orders a different amount of the product from the factories, and each of the 3 factories has a different amount of the product available to ship to the stores. shipping costs per unit of product, factory capacity, and store demand (order amount) are shown in the table below.
store 1 store 2 store 3 factory capacity
factory 1 $4 $1 $7 60
factory 2 $6 $2 $2 200
factory 3 $3 $4 $3 130
store demand 110 40 240

a) find the optimal amount of product to ship from each factory to each store in order to minimize total shipping costs while fulfilling each store’s order.
b) analysts at gamma industries have found that store demand is not constant from month to month. they characterize demand at each store with a triangular distribution, as follows:
min average max
store 1 89 110 121
store 2 36 40 50
store 3 200 240 300

use this information in a model to answer the following questions, based on the shipping plan you found in part (a).
b1) what is the likelihood of stockouts at each of the stores?
b2) what is the likelihood of excess inventory at each of the stores?
describe what additional data would you need to collect, and how would you modify this new model to find a shipping plan that minimized total costs.

c) explain two challenges you might face in getting management to accept and use your results.
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