A manufacturing firm operates three factories—Factory A, Fac…
A manufacturing firm operates three factories—Factory A, Factory B, and Factory C—that distribute goods to four retail stores. Each factory has a specific daily production capacity and may ship goods to any of the four stores. However, the total production capacity across all factories exceeds the total daily demand of the stores. Because the company does not have storage facilities, any unused capacity results in idle resources and should be minimized if possible. Factory A can produce up to 250 units per day, Factory B can produce 250 units, and Factory C can produce 200 units. The daily demand at the four stores is as follows: Store 1 requires 180 units, Store 2 requires 160 units, Store 3 requires 120 units, and Store 4 requires 140 units. The cost (in dollars) to ship one unit from each factory to each store is given in the table below: Shipping Cost per Unit ($) Store 1 Store 2 Store 3 Store 4 Factory A $4 $6 $9 $5 Factory B $7 $5 $4 $6 Factory C $6 $8 $3 $7 Determine the optimal shipping quantities from each factory to each store in order to minimize the total transportation cost, while ensuring that each store’s demand is fully met and no factory exceeds its daily production capacity. At the optimal solution, how many units should Factory B produce to meet the distribution plan? units At the optimal solution, how many units should Factory B ship to Store 2? units What is the minimum total shipping cost required to satisfy all store demands? $