A company has a vertical storage system with three storage tanks at different levels: top, middle, and bottom. Each tank level has capacity limits on both weight and space, as summarized in the following table:

Tank level	Weight Capacity (Tons)	Space Capacity (Cubic feet)
Top	180	50,000
Middle	220	70,000
Bottom	350	90,000

Furthermore, the weight of the goods in each tank must be with the same proportion to its corresponding maximum weight capacity in order to maintain the balance of the storage system, such that

weight of goods on the bottom tank	=	weight of goods on the middle tank	=	weight of goods on the top tank
weight capacity of the bottom tank		weight capacity of the middle tank		weight capacity of the top tank

The following four goods have been offered for storage as space is available:

Good	Weight (Tons)	Volume (Cubic feet=Ton)	Profit ($=Ton)
A	2.0	550	300
B	1.6	750	380
C	25	650	350
D	4.0	450	280

Any portion of these goods can be accepted, and multiple goods can be stored in the same tank. The objective is to determine how much (if any) of each good should be accepted and how to distribute each among the tanks to maximize the total profit for the company.

a) Formulate a LP model for this problem. b) Solve this model using the solver in Excel. c) Is it a good idea to put Good D onto the top tank? Justify your answer using the sensitivity report.