A couple wants to invest up to

Question

$
60000
$60000. They can purchase a type A bond yielding
9.25
%
9.25% return and a type B bond yielding a
12.5
%
12.5% return on the amount invested. They also want to invest at least as much in the type A bond as in the type B bond. They will also invest at least
$
30000
$30000 in type A and no more than
$
36000
$36000 in type
B
B bond.
How much should they invest in each type of bond to maximize their return?
Let
x
x be the amount invested in type
A
A bond and
y
y the amount invested in type
B
B bond. a) Write the objective function to be maximized. b) The feasible region has 3 corner points. List the three corner points. c) Determine the amount to be invested in each bond to maximize the return and determine the maximum return: Amount to be invested in type
A bonds \$
Amount to be invested in type
B bonds \$ Maximum return is

Answer 1

a) The objective function to be maximized is the return on investment. Let R represent the return on investment.

b) The feasible region has 3 corner points. The corner points are:
- (30000, 30000)
- (36000, 30000)
- (36000, 36000)

c) To determine the amount to be invested in each bond to maximize the return, we can set up a linear programming problem.

Let x be the amount invested in type A bond and y be the amount invested in type B bond.

The constraints are:
- 30000 ≤ x ≤ 36000
- 0 ≤ y ≤ 60000
- x ≥ y

The objective is to maximize the return, which can be calculated as:
R = 0.0925x + 0.125y

To solve this linear programming problem, we can graph the feasible region and find the corner point that results in the maximum return.

The three corner points are:
- (30000, 30000)
- (36000, 30000)
- (36000, 36000)

By substituting the values of the corner points into the objective function, we can calculate the returns:
- R1 = 0.0925(30000) + 0.125(30000)
- R2 = 0.0925(36000) + 0.125(30000)
- R3 = 0.0925(36000) + 0.125(36000)

By comparing the returns, we can determine the maximum return and the corresponding investment amounts.

The amounts to be invested in each bond to maximize the return are:
- Amount to be invested in type A bonds: $36000
- Amount to be invested in type B bonds: $30000

The maximum return is:
- Maximum return is R3 = 0.0925(36000) + 0.125(36000) = $9270