12. (***) (Microsoft Excel problem) Consider the following information: PLANT B Total CAPACITY 400 500 100 1.000 STORE X Y z Total DEMAND 200 250 300 750 Cost to shop from plant to store (per unit of demand) Store PLANT B $2.00 $4.00 $3.00 $2.00 $5.00 $3.00 $3.50 $450 53.00 a. Write out the assignment problem by hand, using Equa- tions (8.4) through (8.7) and Example 8.7 as a guide. b. Develop an Excel spreadsheet that uses the Solver func- tion to find the optimal shipping patterns between the plants and the stores. (Hint: The objective function for the optimal solution is $2,200.) Interpret your answer. Is there any plant that is underutilized? If so, why do you think this is the case? How might you use this information in any future decision to expand plant capacities