(***) (Microsoft Excel problem) Consider the following information: PLANT CAPACITY STORE DEMAND A 400 X 200 B 500 Y 250 C 100 Z 300 Total: 1,000 Total: 750 Cost to shop from plant to store (per unit of demand) STORE PLANT X Y Z A $2.00 $2.00 $3.50 B $4.00 $5.00 $4.50 C $3.00 $3.00 $3.00 a. Write out the assignment problem by hand, using Equations (8.4) through (8.7) and Example 8.7 as a guide. b. Develop an Excel spreadsheet that uses the Solver function 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?