# Regal Investments has just received instructions from a client to invest in two shares; one an airline share, the other an insurance share. The total...

Regal Investments has just received instructions from a client to invest in two shares; one an airline share, the other an insurance share. The total maximum appreciation in share value over the next year is to be maximized subject to the following restrictions:

- the total investment shall not exceed Sh.100,000

- at most Sh.40,000 is to be invested in the insurance shares

- quarterly dividends must total at least Sh.2,600

The airline share is currently selling for Sh.40 per share and its quarterly dividend is Sh.1 per share. The insurance share is currently selling for Sh.50 per share and the quarterly dividend is Sh.1.50 per

share. Regal's analysts predict that over the next year, the value of the airline share will increase by Sh.2 per share and the value of the insurance share will increase by Sh.3 per share.

A computer software provided the following part solution output:

Objective Function Value = 5,400

Required:

a) Formulate the above problem.

b) Explain what reduced cost and dual prices columns above mean.

c) How should the client‟s money be invested to satisfy the restrictions?

d) Suppose Regal‟s estimate of the airline shares appreciation is an error, within what limits

must the actual appreciation lie for the answer in (c) above to remain optimal?

## Answers

b) Reduced cost represents the amount that objective function coefficient of a non-basic decision variable must improve (increase in this case) to be put into the basis. In this case since reduced cost is equal to zero for both variables, it means they are in the basis.

Dual prices on the other hand mean the amount that share appreciation will improve in case any of the

limiting constraints is increased by one unit. This occurs for constraints that the slack is exactly zero. In this case total investment and investment in insurance do have positive dual prices while Dividends does have zero dual price (can not increase share appreciation if increased by one unit).

c) From the computer solution, the client?s money should be invested as follows, to satisfy the restrictions:

1500 shares to be invested in Airline shares, and 800 shares to be invested in insurance shares, to give an optimum quarterly share appreciation of sh. 5400.

d) For the optimal decision to remain the airline shares appreciation should not be lower than 2.5, but can be any higher amount. That is, the optimum solution is insensitive to increase in the share appreciation.

raphael answered the question on

*January 11, 2019 at 06:29*

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