Question

(1 point) A couple wants to invest up to $60000. They can purchase a type A bond yielding 9.5% return and a type B bond yielding a 12% 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 in type A and no more than $48000 in type B bond. How much should they invest in each type of bond to maximize their return? Let x be the amount invested in type A bond and y the amount invested in type B bond. a) Write the objective function to be maximized. b) The feasible region has 3 corner points. List the three points: 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

The objective function is

maximize p = 0.095x + 0.12y

subject to

x + y <= 60000

x >= 30000

y <= 48000

The least value of x would be 30000 and that of y would be 0

The highest value of x would be 60000 when y = 0

When x = 30000, then y = 30000 or 0

Thus the three corner points to be considered are

1. x = 30000 and y = 0
2. x = 30000 and y = 30000
3. x = 60000 and y = 0

The corresponding yield would be

a. x = 30000 and y = 0, yield = 2850

b. x = 30000 and y = 30000, yield = 6450 maximum

c, x = 60000 and y = 0, yield = 5700

Answer:

Amount invested in A bond = $ 30000

Amount invested in B bond = $ 30000

Total yield obtained = $ 6450