Engineering Optimization: Theory and Practice, Fourth Edition

Problems 587

Thermal Station,i

Return function,Ri(x) 1 2 3

Ri(0) 0 0 0

Ri(1) 2 1 3

Ri(2) 4 5 5

Ri(3) 6 6 6

Find the investment policy for maximizing the total electric power generated.

9.10 Solve the following LP problem by dynamic programming:

Maximizef (x 1 , x 2 )= 10 x 1 + 8 x 2

subject to

2 x 1 +x 2 ≤ 25

3 x 1 + 2 x 2 ≤ 45

x 2 ≤ 10

x 1 ≥ 0 , x 2 ≥ 0

Verify your solution by solving it graphically.

9.11 A fertilizer company needs to supply 50 tons of fertilizer at the end of the first month,
70 tons at the end of second month, and 90 tons at the end of third month. The cost of
producingxtons of fertilizer in any month is given by $(4500x+ 20 x^2 ). It can produce
more fertilizer in any month and supply it in the next month. However, there is an
inventory carrying cost of $400 per ton per month. Find the optimal level of production
in each of the three periods and the total cost involved by solving it as an initial value
problem.

9.12 Solve Problem 9.11 as a final value problem.

9.13 Solve the following problem by dynamic programming:

Maximize

di≥ 0

∑^3

i= 1

di^2

subject to

di=xi+ 1 −xi, i= 1 , 2 , 3

xi= 0 , 1 , 2 ,... , 5 , i= 1 , 2

x 3 = 5 , x 4 = 0