Suppose that an investor wants to invest up to 10,000. She plans to buy on speculative type of stock and one conservative type. The speculative stock is paying 12% return, while the conservative stock is paying a 9% return. She has decided to invest at least $2000 in the conservative stock and no more than $6000 in the speculative stock. Furthermore, she does not want the speculative investment to exceed the conservative one. How much should she invest at each rate to maximize her return?

Question

Suppose that an investor wants to invest up to 10,000. She plans to buy on speculative type of stock and one conservative type. The speculative stock is paying 12% return, while the conservative stock is paying a 9% return. She has decided to invest at least $2000 in the conservative stock and no more than $6000 in the speculative stock. Furthermore, she does not want the speculative investment to exceed the conservative one. How much should she invest at each rate to maximize her return?

Answer 1

so. we have

s+c <= 10000
r = .12s + .09c
c >= 2000
s <= 6000
s <= c

we want to maximize r

Feeding all this into our favorite linear programming calculator, we find that 5000 in each place maximizes return.

Answer 2

To solve this problem, we can use a linear programming approach. First, let's define the variables:

Let x be the amount invested in the speculative stock.
Let y be the amount invested in the conservative stock.

We want to maximize the return, so our objective function will be:

Maximize R = 0.12x + 0.09y

Now let's set up the constraints based on the given conditions:

1. Total investment cannot exceed $10,000:
x + y ≤ 10,000

2. Amount invested in the conservative stock should be at least $2000:
y ≥ 2000

3. Amount invested in the speculative stock should be no more than $6000:
x ≤ 6000

4. The speculative investment should not exceed the conservative one:
x ≤ y

Now we have our objective function and constraints. To solve this linear programming problem, we can use graphical methods or software like Excel, Python, or Solver.

Using a graphical approach, we can plot the feasible region defined by the constraints and find the corner points of this region. Then we substitute these corner points into the objective function to evaluate the maximum return.

Alternatively, we can use software like Excel or Python to solve this problem. In Excel, you can use the Solver function to set up and solve the linear programming problem. In Python, you can use libraries like scipy or pulp to solve linear programming problems.

By solving this problem, you will find the optimal values for x and y that maximize the return.