An entrepreneur has a fixed sum of money to invest. He can invest it in a productive investment, which will yield a profit in one year's time that is an increasing, strictly concave function of the amount invested. Or, he can put it in the bank, which will pay him a fixed rate of interest in one year's time. He can also borrow from the bank at the same interest rate, against the promise to repay out of future profits. Formulate and solve the problem of choosing the amount of productive investment and borrowing or lending from the bank, to maximize total income available in one year's time.