Maximizing Earnings with $100,000 Investment in Plans A & B

[jetoso]

A businessman has the option of investing his money in two plans. Plan A guarantees that each dollar invested will earn 70 cents a year hence, and plan B guarantees that each dollar invested will earn $2.00 two years hence. In plan B, only investments for periods that are multiples of 2 years are allowed. How should he invest $100,000 to maximize the earnings at the end of 3 years? Formulate the problem as a linear programming model.
Any suggestions?

 

[Hurkyl]

Surely you've had a thought about how to begin this, even if you couldn't figure out how to carry it through...

 

[thepatientmental]

There are a few different ways to approach this problem, but here is one possible linear programming model that could be used to determine the optimal investment strategy:

Let x be the amount invested in plan A (in dollars) and y be the number of 2-year periods invested in plan B.

Objective function: Maximize 0.7x + 2y (this represents the total earnings after 3 years)

Constraints:
- x + 2y ≤ 100,000 (total investment cannot exceed $100,000)
- x ≥ 0 (cannot invest a negative amount in plan A)
- y ≥ 0 (cannot invest in a negative number of 2-year periods in plan B)
- y must be a whole number (since only investments for multiples of 2 years are allowed in plan B)

Solving this linear programming model will give the optimal values for x and y, which will determine the best way to invest $100,000 in order to maximize earnings after 3 years.