1 ELECTRIC GENERATOR 3 An electrical utility needs to gemerate 6,500 megawatt-hr

Question

1 ELECTRIC GENERATOR 3 An electrical utility needs to gemerate 6,500 megawatt-hr of electricity today. It has 5 generators. If any electricity is generated by a given generator, that generator must be started up and a fixed start-up cost is incurred. 5 There is an additional cost for each megawatt-hr generated by a generator 6 These costs, as well as the maximum capacity of each generator, are shown in the below table Gencrator S3.000 $2.000 $2.500 $1.500 $1.000 $6 LO Fixed start-up cost t-hr S5 S4 $6 $7 12 Maximum capacity (MW-hr) 2.100 00 2.500 1.500 3.000 13 4 The objective is to determine the minimum cost plan that meets the electrical needs today 16 Develop a linear model to determine the minimum cost plan 17 18

Explanation / Answer

Let the MW-hr energy by A = a

Let the MW-hr energy by B = b

Let the MW-hr energy by C = c

Let the MW-hr energy by D = d

Let the MW-hr energy by E = e

Cost of operating A = 3000 + 5a

Cost of operating B = 2000 + 4b

Cost of operating C = 2500 + 6c

Cost of operating D = 1500 + 6d

Cost of operating E = 1000 + 7e

Total Cost = 10,000 + 5a + 4b + 6c + 6d + 7e [ojective function]

Constraints:

(i) a + b + c + d + e >= 6500

(ii) 0 < a <= 2100

(iii) 0 < b <= 1800

(iv) 0 < c <= 2500

(v) 0 < d <= 1500

(vi) 0 < e <= 3000

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