You have:
Max (.06*B + .12*G + .20*S) subject to:
B+G+S = 90,000
G+S <= 22,500
G >= 15,000
You could set this up as a linear programming problem. However, getting to the optimal solution is obvious.
G=15,000, S=7500, B=the remainder
I just need to know how to set up the constraints and objective function. This is a case and a big part of my grade! THANKS!!
Max (.06*B + .12*G + .20*S) subject to:
B+G+S = 90,000
G+S <= 22,500
G >= 15,000
You could set this up as a linear programming problem. However, getting to the optimal solution is obvious.
G=15,000, S=7500, B=the remainder
Let:
- X1 = investment in blue chip stocks (in dollars)
- X2 = investment in growth stocks (in dollars)
- X3 = investment in speculative stocks (in dollars)
Now, let's set up the constraints:
1. Total investment constraint: The man has decided to invest at most $90,000. So, the total investment should not exceed $90,000.
X1 + X2 + X3 ≤ 90,000
2. Percentage constraint: The investment in growth and speculative stocks should not exceed 25% of the total investment.
(X2 + X3) ≤ 0.25 * (X1 + X2 + X3)
3. Minimum investment constraint: At least $15,000 should be invested in growth stocks.
X2 ≥ 15,000
4. Non-negativity constraint: The investment cannot be negative.
X1, X2, X3 ≥ 0
Now, let's define the objective function:
The objective is to maximize the return on investment. The returns from each type of stock investment can be calculated by multiplying the investment amount by the respective returns:
Total Return = 0.06 * X1 + 0.12 * X2 + 0.20 * X3
Therefore, the objective function is:
Maximize Z = 0.06 * X1 + 0.12 * X2 + 0.20 * X3
By formulating the problem with these constraints and the objective function, you can use linear programming techniques to find the optimal solution that maximizes the return.