John Sweeney is an investment advisor who is attempting to construct an "optimal portfolio" for a client who has $400,000 cash to invest. There are ten different investments, falling into four broad categories that John and his client have identified as potential candidates for this portfolio.
The following table lists the investments and their important characteristics. Note that Unidyde Equities (stocks) and Unidyde Debt (bonds) are two separate investments, whereas First General REIT is a single investment that is considered both an equities and a real estate investment.
Formulate and solve a linear program to accomplish John's objective as an investment advisor which is to construct a portfolio that maximizes his client's total expected after-tax return over the next year, subject to a number of constraints placed upon him by the client for the portfolio:
1.Its (weighted) average liquidity factor must be at least 65.
2.The (weighted) average risk factor must be no greater than 55.
3.At most, $60,000 is to be invested in Unidyde stocks or bonds.
4.No more than 40% of the investment can be in any one category except the money category.
5.No more than 20% of the investment can be in any one investment except the money market fund.
6.At least $1,000 must be invested in the money market fund.
7.The maximum investment in All Saver's Certificates is $15,000.
8.The minimum investment desired for debt is $90,000.
9.At least $10,000 must be placed in a T-Bill account.

Question

John Sweeney is an investment advisor who is attempting to construct an "optimal portfolio" for a client who has $400,000 cash to invest. There are ten different investments, falling into four broad categories that John and his client have identified as potential candidates for this portfolio.
The following table lists the investments and their important characteristics. Note that Unidyde Equities (stocks) and Unidyde Debt (bonds) are two separate investments, whereas First General REIT is a single investment that is considered both an equities and a real estate investment.  ​
Formulate and solve a linear program to accomplish John's objective as an investment advisor which is to construct a portfolio that maximizes his client's total expected after-tax return over the next year, subject to a number of constraints placed upon him by the client for the portfolio:
1.Its (weighted) average liquidity factor must be at least 65.
2.The (weighted) average risk factor must be no greater than 55.
3.At most, $60,000 is to be invested in Unidyde stocks or bonds.
4.No more than 40% of the investment can be in any one category except the money category.
5.No more than 20% of the investment can be in any one investment except the money market fund.
6.At least $1,000 must be invested in the money market fund.
7.The maximum investment in All Saver's Certificates is $15,000.
8.The minimum investment desired for debt is $90,000.
9.At least $10,000 must be placed in a T-Bill account.

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The Answer of John Sweeney is an investment advisor who is attempting to construct an "optimal portfolio" for a client who has $400,000 cash to invest. There are ten different investments, falling into four broad categories that John and his client have identified as potential candidates for this portfolio.
The following table lists the investments and their important characteristics. Note that Unidyde Equities (stocks) and Unidyde Debt (bonds) are two separate investments, whereas First General REIT is a single investment that is considered both an equities and a real estate investment.  ​
Formulate and solve a linear program to accomplish John's objective as an investment advisor which is to construct a portfolio that maximizes his client's total expected after-tax return over the next year, subject to a number of constraints placed upon him by the client for the portfolio:
1.Its (weighted) average liquidity factor must be at least 65.
2.The (weighted) average risk factor must be no greater than 55.
3.At most, $60,000 is to be invested in Unidyde stocks or bonds.
4.No more than 40% of the investment can be in any one category except the money category.
5.No more than 20% of the investment can be in any one investment except the money market fund.
6.At least $1,000 must be invested in the money market fund.
7.The maximum investment in All Saver's Certificates is $15,000.
8.The minimum investment desired for debt is $90,000.
9.At least $10,000 must be placed in a T-Bill account.

John Sweeney Is an Investment Advisor Who Is Attempting to Construct