The government of Ghana has available GH¢1 billion earmarked for financing the Free SHS next year. Instead of letting th

[answerhappygod]

The government of Ghana has available GH¢1 billion earmarked for
financing the Free SHS next year. Instead of letting this money sit
in a bank account for a paltry 6% risk free interest rate, it has
decided to invest half of the money in four stocks on the Ghana
Stock Exchange (GSE). The four stock options the government is
considering and the relevant financial data are as follows:

Stock
A B C D
Price Per Share (in GH¢) 100 50 80 40
Annual Return (in GH¢) 18 6 8 8
Possible Loss Per Share (in GH¢) 10 6 6 5

However, the annual return is only a forecast (provided by experts
at the ministry of finance), and could be worse or better – a risk
that the government has been advised to be worry of in order not to
jeopardize the finances of the Free SHS program. For example,
though a share of stock A could yield a return amount of GH¢18, it
is also likely it could lead to a loss of GH¢10.
In order to minimize the risk (i.e. losses) associated with
investing on the GSE, the Finance Ministry has advised the
government to adhere to the following guidelines:
(1) The total forecasted annual return for the four stocks must be
at least 9% of the total amount invested to justify the investment.
Also, total possible losses must not exceed 8% of the total amount
invested.
(2) The amount invested in stock A and Stock C must not exceed
GH¢200 million since when one performs better (worse) the other
also performs better (worse). Likewise, the amount invested in
Stock B and D must not exceed GH¢350 million for the same reason as
that of Stock A and C.
(3) Although Stock A carries a risk of a loss of GH¢10, the
government is willing to buy at least 500,000 shares given the high
return of GH¢18 per share.

i. Formulate a linear program to determine the number of shares of
each stock the government should buy in order to minimize the risk
involve. Note that the government is not obliged to spend all the
money intended for investment. (10 marks)

ii. How many shares of each stock should be bought given the
objective and the constraints, and what is the total possible loss
that could occur? (5 marks)

iii. Will the allocation change if the objective coefficient value
for Stock B is decreased by GH¢3? Explain. (3 marks)

iv. What will happen to the possible total loss if the total annual
return requirement were to be raised by GH¢10,000,000? (4
marks)

v. Interpret the reduce cost for Stock C. (3 marks)