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Find the values of a ∈R for which ia is a solution of 0 z z2 z7 z4 10 4 3 2
− + − + = .
Also find all the roots of this equation.
− + − + = .
Also find all the roots of this equation.
a grocery shop sell milk packets containing half a litre of milk. it makes bulk purchase of the same from the nearby city. every time a purchase is made, it incurs a cost of Rs 50 towards transportation. the daily demand of packets is about 250. the holding cost is Rs 0.10 for a packet per day to preserve it in a refrigerator. determine the optimum quantity of a bulk purchase and a cycle time.
solve the following integer linear programming problem
max 2x_1 + 5x_2 + 7x_3
subject to
4x_1 + 3x_2 + x_3 >= 29
where x_1, x_2 and x_3 are non negative integers
max 2x_1 + 5x_2 + 7x_3
subject to
4x_1 + 3x_2 + x_3 >= 29
where x_1, x_2 and x_3 are non negative integers
The cost vector in a LPP becomes an activity vector in its dual problem.
plz tell whether these statements are true or false with justification:--
(i) For a transportation problem with 4 origins and 5 destinations, the maximum number
of basic cells is 9.
(ii) If the LP relaxation of an integer linear programming problem has a feasible solution,
the integer linear programming problem also has a feasible solution.
(iii) In a project network diagram, the critical path is the longest among all paths
(i) For a transportation problem with 4 origins and 5 destinations, the maximum number
of basic cells is 9.
(ii) If the LP relaxation of an integer linear programming problem has a feasible solution,
the integer linear programming problem also has a feasible solution.
(iii) In a project network diagram, the critical path is the longest among all paths
Calculate the divergence of the vector function rre Fˆsin2q=r
a) Find the values of aÎR for which a i is a solution of z 2z 7z 4z 10 0 4 3 2 − + − + = .
Also find all the roots of this equation. (5)
b) Find all the 8th roots of 3i − 3. Also show any one of them in an Argand diagram.
Also find all the roots of this equation. (5)
b) Find all the 8th roots of 3i − 3. Also show any one of them in an Argand diagram.
Obtain the resolvent cubics, by Descartes’ method and by Ferrari’s method, of the
equation x 4x 8 0 4 3 + + = . Are the cubics the same? Further, use either method to
obtain the roots of this equation.
equation x 4x 8 0 4 3 + + = . Are the cubics the same? Further, use either method to
obtain the roots of this equation.
A solid of revolution is formed by rotating about the x-axis the area bounded between
x = ,0 x = 1 and the curve given by the table
x- f(x)
0 - 1.0
0.25 - 0.98965
0.5 - 0.9587
0.75 - 0.9089
1.0- 0.841
Find the volume of the solid so formed using
i) Trapezodial rule ii) Simpson’s rule
x = ,0 x = 1 and the curve given by the table
x- f(x)
0 - 1.0
0.25 - 0.98965
0.5 - 0.9587
0.75 - 0.9089
1.0- 0.841
Find the volume of the solid so formed using
i) Trapezodial rule ii) Simpson’s rule
Consider the following data
x - f(x)
1.0 - 0.7651977
1.3 - 0.6200860
1.6 - 0.4554022
1.9 - 0.2818186
2.2- 0.1103623
Use Stirling’s formula to approximate f(1.5) with x0 = 1.6
x - f(x)
1.0 - 0.7651977
1.3 - 0.6200860
1.6 - 0.4554022
1.9 - 0.2818186
2.2- 0.1103623
Use Stirling’s formula to approximate f(1.5) with x0 = 1.6
