Solve the linear programming problems in Problem 21-36 by applying the simplex method to the dual problem. Minimize C = 6 x 1 + 8 x 2 + 3 x 3 subject to − 3 x 1 − 2 x 2 + x 3 ≥ 4 x 1 + x 2 − x 3 ≥ 2 x 1 , x 2 , x 3 ≥ 0
Solve the linear programming problems in Problem 21-36 by applying the simplex method to the dual problem. Minimize C = 6 x 1 + 8 x 2 + 3 x 3 subject to − 3 x 1 − 2 x 2 + x 3 ≥ 4 x 1 + x 2 − x 3 ≥ 2 x 1 , x 2 , x 3 ≥ 0
Solution Summary: The author explains that the optimal solution of the minimization problem cannot be determined through simplex tableau.
Calculate a = x+y, b = z + 1, then keep numbers a and b.
Questions marked with *** are to be graded.
1. Use the initial and final value theorems to determine x(0*) and x(oo) for the following
transforms:
a(s+2)
***
a) X(s)=
s(s+b)
2(s+2)
b) X(s)=
s(s+a)(s+b)
2. Obtain the inverse Laplace transform for the following transforms.
a) F(s)=
as+b
b) F(s)=
5s+2
(s+a)(s+b)²
3. Obtain the solution x(t) of the the following differential equations:
a) x+ax=0, x(0)=b, x(0) = 0
b) 2x+2x+x=a, x(0)=0, x(0)=b
4. Obtain the inverse transform of the following. If the denominator of the transform has
complex roots, express x(t) in terms of sin() and cos().
***
a) X(s)=
b) X(s)=
4s+a
+8s+b
s³+as+6
s(s+b)
5. Determine the unit-step response, f (t) = u(t) of the following models. Take zero initial
conditions.
a) ax+20x+bx = f(t)
b) x+ax+bx=3f(t)+2f(t)
In a survey, the planning value for the population proportion is p 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error
of 0.03? Round your answer up to the next whole number.
800
{
Q/ calculate the Fourier series of f(x) on the given
interval
f(x) = x Sin X
9
-
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