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Q. Solve this degeneracy problem
11 〖2 〗^8 8 〖6 〗^6 〖2 〗^4 Supply
〖9 〗^10 9 12 9 6 18
7 6 〖3 〗^8 7 7 10
〖9 〗^2 3 5 〖6 〗^2 11 8
Demand 12 8 8 8 4 4
11 〖2 〗^8 8 〖6 〗^6 〖2 〗^4 Supply
〖9 〗^10 9 12 9 6 18
7 6 〖3 〗^8 7 7 10
〖9 〗^2 3 5 〖6 〗^2 11 8
Demand 12 8 8 8 4 4
Q. Solve this degeneracy problem
Dealer 1 2 3 4 Supply
A 2 2 2 4 1000
B 4 6 4 3 700
C 3 2 1 0 900
Demand 900 800 500 400
Dealer 1 2 3 4 Supply
A 2 2 2 4 1000
B 4 6 4 3 700
C 3 2 1 0 900
Demand 900 800 500 400
Q.Solve by NWCM (north-west corner method) and find optimal solution by UV method
3 1 7 4 Supply
2 6 5 9 250
8 3 3 2 350
Demand 200 300 350 400
3 1 7 4 Supply
2 6 5 9 250
8 3 3 2 350
Demand 200 300 350 400
Q. Solve by least cost method and apply UV method to optimize the solution.
19 30 50 13 Supply
70 30 40 60 7
40 10 60 20 10
Demand 5 8 7 15 18
19 30 50 13 Supply
70 30 40 60 7
40 10 60 20 10
Demand 5 8 7 15 18
Q. Solve the given problem by NWCM (north-west corner method), LCM (the least cost method) and VAM (Vogel's approximation method) and find optimal solution by UV method.
11 13 17 14 Supply
16 18 14 10 250
21 24 13 10 300
Demand 200 225 275 400
11 13 17 14 Supply
16 18 14 10 250
21 24 13 10 300
Demand 200 225 275 400
Sum of a pair of two integers is 2017. If the largest number is not greater than
1100 what is the possible number of pairs?
1100 what is the possible number of pairs?
The value of a three digit number increases by 108 when the first digit is palced at
the last and the value of the number increases by 189 when the last number is
placed at the first. Determine the summation of all the possible numbers.
the last and the value of the number increases by 189 when the last number is
placed at the first. Determine the summation of all the possible numbers.
GCD(100,GCD(101, GCD(102, … GCD(149,150))…) = ?
charging and discharging characteristics of DC
(a) Here is the information about the circuit.
Capacitor = 100 nF , Resistor = 47 kΩ ,Supply voltage = 5 V
Charging characteristic for a series capacitive circuit:
v=v(1 − e−t/RC)
Investigate what the other terms in this expression mean.
Calculate the time constant for the circuit.
Use a spreadsheet to plot the charging curve over the range 0 to
20 ms (milliseconds).
Investigate the meaning of ‘time constant’ and from your graph
estimate a value. Compare this with your calculated one.
Differentiate the charging equation and find the rate of change of
voltage at 6 ms.
From your graph measure the gradient at 6 ms and compare this with
the calculated value.
(b) Now investigate the discharging characteristic of the circuit but with a 22 kΩ resistor
fitted.
Calculate and estimate the rate of change of voltage when t = T.
(a) Here is the information about the circuit.
Capacitor = 100 nF , Resistor = 47 kΩ ,Supply voltage = 5 V
Charging characteristic for a series capacitive circuit:
v=v(1 − e−t/RC)
Investigate what the other terms in this expression mean.
Calculate the time constant for the circuit.
Use a spreadsheet to plot the charging curve over the range 0 to
20 ms (milliseconds).
Investigate the meaning of ‘time constant’ and from your graph
estimate a value. Compare this with your calculated one.
Differentiate the charging equation and find the rate of change of
voltage at 6 ms.
From your graph measure the gradient at 6 ms and compare this with
the calculated value.
(b) Now investigate the discharging characteristic of the circuit but with a 22 kΩ resistor
fitted.
Calculate and estimate the rate of change of voltage when t = T.
The function f(x) satisfies the equation f(x) = f(x−1)+f(x+1) for all values
of x. If f(1) =1 and f(2) = 3, what is the value of f(2013)?
of x. If f(1) =1 and f(2) = 3, what is the value of f(2013)?
