University of Essex is considering eliminating the use of trays in the university campus’ cafeteria as a way of reducing energy costs and fulfilling the university’s Sustainability Sub-Strategy (SSS). The University has spent £40,000 in the purchase of 20,000 trays for the campus’ cafeteria. Advocates argue that the fewer the number of trays used, the lower will be the costs of cleaning the trays, resulting in savings on water and overall energy usage. Based on an experiment conducted in 2019 in which students were asked to voluntarily reduce their use of trays, the university was able to estimate the annual cost savings associated with varying levels of cooperation, and are given in the table below. In the experiment, however, it became clear that as students used fewer trays, additional help was needed to bus tables and clean them after meal periods were over. Additional labour costs were estimated to be an additional £20.00 for every tray no longer used. Also, higher energy costs were needed to keep the cafeteria open and lighted to clean it, amounting to £500 per 100 trays reduced annually.

Number of Trays No Longer Used	Total Cost Savings
5,000	100,000
6,000	190,000
7,000	270,000
8,000	340,000
9,000	400,000
10,000	450,000
11,000	490,000
12,000	520,000
13,000	540,000
14,000	550,000

With reference to the data obtained from the experiment on the number of trays no longer used and total cost savings above, you are asked to write a short report that includes: 

a) describing the marginal analysis you conduct and present your estimates of MB, TC, MC, and NB together with data provided in a table, 

b) determining the optimal level of activity with justification the University should aim for in order to best serve its SSS, and c) explaining why.