In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method. Investment. An investor has $ 60 , 000 to invest in a CD and a mutual fund. The CD yields 5 % and the mutual fund yields an average of 9 % . The mutual fund requires a minimum investment of $ 10 , 000 , and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the return? What is the maximum return?
In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method. Investment. An investor has $ 60 , 000 to invest in a CD and a mutual fund. The CD yields 5 % and the mutual fund yields an average of 9 % . The mutual fund requires a minimum investment of $ 10 , 000 , and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the return? What is the maximum return?
In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method.
Investment. An investor has
$
60
,
000
to invest in a CD and a mutual fund. The CD yields
5
%
and the mutual fund yields an average of
9
%
. The mutual fund requires a minimum investment of
$
10
,
000
, and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the return? What is the maximum return?
Prove let Aand B submodul of M
A is large sub podule A large of B
and B large of M.
SM
B Smale sub module B/A smal of M/A
and As Mallof M.
Give example and expleain caim.
Amonorphism and split
d) Determine the following group: Hom, (Q,Z)
and Ho M₂ (Q, Q) and Hom (2/12, Q) =
Q2: Using the Laplace transform, find the solution for the following equation
y"" +y" = 6et + 6t + 6. Suppose zero initial conditions (y"" (0) = y"(0) = y'(0) = y(0) = 0).
1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
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