Management science in action at Gringo Mutual Fund

Gringo Asset Management $($GAM$)$ located in Lobatse has a staff compliment of $50.$ It provides a suite

of services to government and private sector clients around the SACU region. In a day, GAM can serve

on average $100$ clients who physically come to its offices and on average $350$ clients through

telephone and internet services. Other than the goal of growing and hedging a client's money, it also

faces different kinds of issues such as skyrocketing operating costs due to global inflation. GAM has

just secured P$200000$ after liquidating its stake in Cresta Hotels which was seemingly affected by

COVID$-19$ crisis. GAM is now in search of new investments opportunities. Specifically, GAM have

identified five investment assets using knowledge from its equity tracker monitor as shown in Table $1.$

Table $1$: Investment opportunities for GAM

The board of GAM have stipulated that:

No more than P$100000$ should be invested in neither resources nor steel sector.

Botswana Retail bonds should have a minimum of $25\%$ of the steel sector allocation.

The investment in Pan Africa diamonds should be a maximum of $60\%$ of the total investment

investments in resource sector.

Average risk factor should not exceed $27.$

Required

a$)$ Identify and discuss the potential kinds of restrictions that a modeler can be faced with when

intending to apply linear programming to optimize GAM's portfolio. $(10$ marks$)$

b$)$ Develop a linear optimization model to minimize risk in the above problem without solving it$.$

$(15$ marks$)$