Formulate the linear programming model for the issue algebraically. Group this in three sections:

1) Definition of Decision Variables, 2) Objective Function Equation, 3) Constraints Equations. Set up and solve this problem using Excel using solver.

Richelieu Specialty Paints has been quite successful and has $1,500,000 cash to be invested. Amanda and her management team have developed four potential investments in addition to leaving the cash in a low interest deposit. The four new opportunities are:

1. Purchase some shares of a major supplier (25% risk of total loss, 13% potential return)

2. Invest in the research and development of a new product (50% risk of total loss, 60% potential return)

3. Buy a selection of corporate bonds (10% risk of total loss, 6% potential return)

4. Buy a selection of government bonds (1% risk of total loss, 3% potential return) Leaving the money in a low interest deposit is virtually riskless and has a 0.5% potential return.

Richelieus father had provided Amanda with some guidelines for investment, aimed at diversification and risk management. These are:

1. Invest a maximum of 40% of the total cash in any one of the four new opportunities to ensure some risk control.

2. Invest at least $100,000 in each of the four new opportunities to ensure some diversity.

3. Limit the total potential loss, on average, to $250,000, based on the risk factors indicated.

4. Ensure the highest return possible.

Recommend the appropriate mix of the four investments and note how much money, if any, should be left in the low interest deposit. Also, how would this mix change, and what would happen to potential return, if Amanda decided to take a more conservative approach and limit the total potential loss to $175,000.