An Investor Wants to Invest $50,000 in Two Mutual Funds

question 26

Essay

An investor wants to invest $50,000 in two mutual funds, A and B. The rates of return, risks and minimum investment requirements for each fund are:
$\begin{array}{cccc}\text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minimum investment } \\\hline \mathrm{A} & 12 \% & 0.5 & \$ 20,000 \\\mathrm{~B} & 9 \% & 0.3 & \$ 10,000\end{array}$
Note that a low Risk rating means a less risky investment. The investor wants to maximize the expected rate of return while minimizing his risk. Any money beyond the minimum investment requirements can be invested in either fund. The investor has found that the maximum possible expected rate of return is 11.4% and the minimum possible risk is 0.32.
Formulate a goal programming model with a MINIMAX objective function.

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Definitions:

α-Amylase

An enzyme that breaks down starches into sugars and is found in saliva and pancreatic fluid, aiding in the digestive process.

Gibberellin

A plant hormone that promotes growth and influences various developmental processes, including stem elongation, germination, and flowering.

Senescence

The process of aging where cells lose the ability to divide, grow, and function, leading to the eventual death of the cell.

Cytokinin

A class of plant hormones that promote cell division and growth, and are involved in aging, nutrient processing, and other physiological processes.