Optimum Performance of a Four Chiller System
Four chillers are used to supply chilled water for cooling purposes Each chiller has a maximum capacity of 1400 tons of refrigeration and has variable load capabilities.
The operating costs for cach chiller
C1 = L12 + 0.35 L1 + 0.02
C2 = 9.55L2² + 0.40 L2 + 1.0
C3 = 2.47 L32 + 8.37 L3 + 2.6
C4 = 2.10 L4² + 8.30 L4 + 2.6
Ci is dollars per hour, L1 is the chiller load in 1000s of tons of refrigeration
The total refrigeration load is:

Lt = L1+L2+L3+L4

The total cost, Ct ($), and average cost, Ctt as a function of demand, Dt

Ct =C1+C2+C3+C4
Ctt C//D

A parallel chiller system operates with equal loading on each chiller. A series chiller system operates sequentially. For total loading of 1 Kton through 5 Ktons, at 500-ton intervals, determine the optimum loading for each chiller and the optimum operating cost.
Generate four graphs
1.) operating costs for individual chiller vs. Load for range of 0 to 1.4 Kton
2.) Optimum Chilller load (0 to 1.4 Kton) vs. total demand (0 to 5 Ktons)
3.) Cost (4/Kton-hr) vs. Total Demand (1 Kton to 5 Kton)
4.) Summary graph of Ctt vs. Demand for
a Series
b. Parallel
C. optimum
You can do the series and parallel parts using Excel or some other equation solver; the optimum part requires Lagrange Multiplier equations
Present your work and a brief summary of your observations (say something intelligent about the results.

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