An investor is considering three types of investments: a high-risk venture into oil leases with a potential return of 15%, a medium-risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. he has $50,000 to invest. because of the risk, he will limit his investment in oil leases and stocks to 30% and his investment in oil leases and bonds to 50%. assuming that investment returns are as expected, how much should be invested in each in order to maximize his return?

let o = the amount invested in oil leases,
let s = the amount invested in stocks, and
let b = the amount invested in bonds

which option (a, b, c, or d) shows the correct objective function and constraints for this application?

objective function: maximize return, r = 15%*o + 9%*s + 5%*b
constraints: o + s + b = 50,000, o + s < = 30%*50,000, o + b < = 50%*50,000, o > = 0, s > = 0, b < = 0

objective function: maximize return, r = 9%*o + 5%*s + 15%*b
constraints: o + s + b = 50,000, o + s < = 30%*50,000, o + b < = 50%*50,000, o > = 0, s > = 0, b < = 0

objective function: maximize return, r = 15%*o + 9%*s + 5%*b
constraints: o + s + b < 50,000, o + s < = 30%*50,000, o + b < = 50%*50,000, o > = 0, s > = 0, b < = 0

objective function: maximize return, r = 15%*o + 9%*s + 5%*b
constraints: o + s + b < 50,000, o + s > = 30%*50,000, o + b > = 50%*50,000, o > = 0, s > = 0, b < = 0