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Use the Table Below to Answer the Following Questions) The Company Recommends That No More Than $300,000 Be Invested

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Use the table below to answer the following questions) .
Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below.  Qualis Mutual Fund Data  Expected Annual  Return  Risk Measure 1 Qualis Low-priced Stock Fund 7.23%11.872 Qualis Multinational Fund 8.42%12.623 Qualis Mid-cap Stock Fund 6.66%13.724 Qualis Mortgage Fund 2.72%3.375 Qualis Income Equity Fund 8.89%8.46 Qualis Balanced Fund 3.50%6.91\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array} The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return of at least 6%. Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.
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Definitions:

Social Welfare Function

A theoretical framework in economics that represents preferences over social states or outcomes, aiming to aggregate individual utilities into a measure of collective welfare.

Pareto Optimum

A distribution of resources in which it is not feasible to rearrange in a way that improves one person's situation without detrimentally affecting at least another individual's standing.

Utility Possibilities Frontier

A graph that shows the maximum amount of utility that can be achieved by different individuals or groups from a fixed set of resources.

Production Possibilities

A curve or frontier that illustrates the maximum feasible amounts of two commodities that can be produced with available resources and technology.

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