This document contains 8 questions related to water resources system planning and management. It provides data for various linear programming, nonlinear programming and dynamic programming problems to maximize or minimize objectives subject to constraints. It also includes questions on simulation, convexity/concavity of functions, and evaluation of different project plans using equivalent worth method.

1. JNTUW
ORLD
Code No: 07A70107 R07 Set No. 2
IV B.Tech I Semester Examinations,December 2011
WATER RESOURCES SYSTEM PLANNING AND MANAGEMENT
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. Use revised simplex (Matrix) method to solve the following linear programming
problem; Maximize
Z = 6x1-2x2+3x3 subject to 2x1+ x2 + 2x3≤ 2; 2x1+ 4x3≤ 4; x1,x2 and x3 ≥ 0.
[16]
2. (a) What is the difference between optimization and simulation in a systems anal-
ysis? Explain ?
(b) Define local maximum, local minimum, saddle point, convexity of a function
of a single variable. [8+8]
3. What is simulation? Describe its advantages in solving the problems. Give its main
limitations with suitable examples. [16]
4. Explain the following terms monopoly value, speculative value, assessed value, scrap
value, salvage value, distress value, replacement value, potential value. [16]
5. (a) Determine how many projects of type A,B and C should be built in order to
maximize the total net return from all projects, given the following data
Project type Cost of each project Net return/project
A 2000 280
B 3000 440
C 4000 650
Total amount available for all projects = 24000 units. At least one project of
each type should be built. Not more than 4 projects of each should be built.
(b) What is the curse of dimensionality? Explain? [10+6]
6. A water resources system consisting of two reservoirs is shown in figure 1. The flows and
storages are expressed in a consistent set of units. The following data are available
:
Quantity Stream1(i=1) Stream 2(i=2)
Capacity of reservoir i 9 7
Available release from reservoir i 9 6
Capacity of channel below reservoir i 4 4
Actual release from reservoir I x1 x2
The capacity of the main channel below the confluence of the two streams is 5
units. If the benefit is equivalent to Rs 200 lakhs and Rs. 300 lakhs per unit of
water released from reservoirs 1 and 2, respectively, formulate a linear programming
problem to maximize the benefit.
16]
1
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2. JNTUW
ORLD
Code No: 07A70107 R07 Set No. 2
7. Maximize f(x1, x2) = 3x2
1 + x2
2 + 2x1x2 + 6x1 + 2x2
Subject to the constraints
2x1 − x2 = 4,
x1, x2 ≥ 0. [16]
8. Discuss the importance of water resources development in India, with special ref-
erence to
(a) Recreation and
(b) Flood control. [16]
2
Figure 1
* * * * * *
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3. JNTUW
ORLD
Code No: 07A70107 R07 Set No. 4
IV B.Tech I Semester Examinations,December 2011
WATER RESOURCES SYSTEM PLANNING AND MANAGEMENT
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) What are the basic techniques used in water resources systems, Explain ?
(b) Examine the following function for Concavity/Convexity and determine their
values at the extreme points f(X) = x1
2 + x2
2 − 4x1 − x2. [6+10]
2. (a) Define the following in a simplex method
i. Unbounded solution
ii. alternate optimum solution
(b) Solve the following Linear Programming problem graphically; minimize
Z =45x1 +55x2 subject to x1 +2x2 ≤ 30; 2x1+3x2≤80; x1-x2≥ 8; x1, x2 ≥ 0.
[8+8]
3. What are single purpose and multipurpose projects? Under what circumstances do
you go for a multipurpose project? Discuss. [16]
4. Solve the following NLPP, showing the necessary and sufficient conditions:
Minimize Z = 3x2
1 + x2
2 + 2x1x2 + 6x1 + 2x2,
Subject to 2x2 − x2 = 4,
x1, x2 ≥ 0. [16]
5. Solve the following LP problem using dual simplex method; Maximize Z = 2x1+x2
subject to x1+2x2≤ 10; x1+x2≤ 6; x1-x2 ≤ 2; x1-2x2≤ 1 ; x1,x2 ≥ 0.
[16]
6. The daily demand for a product is normally distributed with a mean of 120 and a
standard deviation of 10. Describe any method to simulate the demand. [16]
7. (a) What is the curse of dimensionality?
(b) A total of 3 units of water is to be allocated optimally to three thermal sta-
tions. The allocation is made in discrete steps of one unit ranging from 0 to 3.
with the three thermal stations denoted as thermal 1, thermal 2 and thermal
3 respectively, the return obtained from the users for a given allocation are
given in the following table. Find allocations to the three thermal stations
such that the total return is maximized using backward recursion of dynamic
programming
3
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4. JNTUW
ORLD
Code No: 07A70107 R07 Set No. 4
Return function Thermal station, i
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
[16]
8. Explain the following terms market value, book value, assessed value, scrap value,
salvage value, distress value, replacement value, potential value. [16]
4
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5. JNTUW
ORLD
Code No: 07A70107 R07 Set No. 1
IV B.Tech I Semester Examinations,December 2011
WATER RESOURCES SYSTEM PLANNING AND MANAGEMENT
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Explain the primal-Dual relationship
(b) State the general rules for formulating dual Problem from its primal.
[8+8]
2. Determine the relative maximum or minimum value (if any) of the following func-
tion:
f(x) =x1 + 2x2 + x1x2 − x2
1 − x2.
2 [16]
3. A bread vendor buys every morning loaves of bread are Re. 0.45 each by placing
his order one day in advance (at the time of receiving his previous order) and sells
them at Rs. 0.70 each. Unsold bread can be sold the next day at Rs. 0.20 per loaf
and discarded thereafter. The pattern of demand for bread is given below:
Daily sales
(Fresh bread): 50 51 52 53 54 55 56 57 58 59 60
Probability
of demand : 0.01 0.03 0.04 0.07 0.09 0.11 0.15 0.21 0.18 0.09 0.02
Daily sales (one day old bread) : 0 1 2 3
Probability of Demand 0.70 0.20 0.08 0.02
The vendor adopts the following order rule: If there is no stock with him at the end
of the previous day, he orders 60 units. Otherwise, he orders 50 or 55 whichever is
nearest the actual fresh bread sale on the previous day. Starting with zero stock
and a pending order for 55 loaves, simulate for 10 days and calculate the vendors
profits. [16]
4. (a) What are the procedures used while analyzing any general system, Explain.
(b) Examine the following function for Concavity/Convexity and determine their
values at the extreme points f(X) = 5x2
1 + 2x − x1x2. [6+10]
5. A sum of 75,000 has been borrowed from a bank at the rate of interest of 8%
per annum for a period of 10 years. Determine the annual payment amount and
payment component and interest. [16]
6. Solve the following Linear programming problem using the simplex method; Max-
imize
Z = x1- 3x2+2x3 subject to 3x1 x2 +3x3≤ 7; -2x1+4x2 ≤ 12;
-4x1+3x2 + 8x3≤ 10; x1,x2, and x3 ≥ 0. [16]
5
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6. JNTUW
ORLD
Code No: 07A70107 R07 Set No. 1
7. Solve the following 4-user water allocation problem to maximize the total returns,
using Backward recursion of dynamic programming : water available for allocation:
60 units, to be allocated in discrete units of 0, 10, 20,.60. Return from the four
users for a given allocation, are given in the table below:
Allocation Returns from
1 2 3 4
0 0 0 -3 1
10 3 4 3 1
20 5 4 5 1
30 6 4 5 7
40 3 4 4 8
50 3 6 2 10
60 3 7 0 10
[16]
8. (a) Describe the organization structure for water planning in our country
(b) Enumerate different methods of cost allocation to multipurpose projects. [16]
6
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7. JNTUW
ORLD
Code No: 07A70107 R07 Set No. 3
IV B.Tech I Semester Examinations,December 2011
WATER RESOURCES SYSTEM PLANNING AND MANAGEMENT
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. What is simulation? Describe the simulation process. What are the reasons for
using simulation? [16]
2. (a) Define stationary point, saddle point for a function of a single variable?
(b) What are the necessary and sufficient conditions to optimize a function of
multiple variables without constraints. [4+12]
3. Solve the following Linear programming problem using the simplex method; Max-
imize
Z = x1+x2+x3 subject to 4x1 +5x2 +3x3≤ 15; 10x1+7x2+x3 ≤ 12; x1,x2, and
x3≥ 0. [16]
4. (a) Describe the principal purpose for which the cost of a multipurpose project is
allowed.
(b) Enumerate different methods of cost allocation to multipurpose projects. [16]
5. Solve the following LP problem using dual simplex method; Minimize Z = x1+2x2+3x3
subject to 2x1-x2+x3≥4; x1+x2+2x3≤ 8; x2-x3≥2; x1,x2 and x3 ≥ 0. [16]
6. For each of the following functions, verify whether it is convex, concave or neither:
(a) f(x) =2x + x2
(b) f(x) =2x3
− x2
[8+8]
7. Inflows during four seasons to a reservoir with storage capacity of 4 units are re-
spectively, 2, 1, 3 and 2 units. Only discrete values, 0,1,2, . are considered for
storage and release. Reservoir storage at the beginning of the year is equal to 4
units. Release from the reservoir during a season results in the following benefits
which are same for all the four seasons
Release Benefits
8 -100
9 250
10 320
11 480
12 520
13 520
14 410
15 120
[16]
7
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8. JNTUW
ORLD
Code No: 07A70107 R07 Set No. 3
8. To execute a project following two plans can be used. Determine the feasibility
of the plan for the execution of the project for the following data with interest rate
of 8% per annum using equivalent worth method
Plan A Plan B
1 Cost of equipment 60,000 40,000
2 Operation and maintenance cost annually 2,500 3,200
3 Salvage value 8,000 7,000
4 Service life 30 years 15 years
[16]
8
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