Determine the amount to be invested in each bond to maximize the return and determine the maximum return?

Question

A couple wants to invest up to $20000. They can purchase a type A bond yielding 9.75% return and a type B bond yielding a 14.5% 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 $10000 in type A and no more than $14000 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.
P =

b) List the corner points of the feasible region.
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) P =0.0975x + 0.145y
b) (10,0), (20,0), (10,10)
c) 10k in A, 10k in B, 975 + 1450 = 2425