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.