Question

Sharon has a total of $190,000 to invest in three types of mutual funds: growth, balanced, and income funds. Growth funds have a rate of return of 12%/year, balanced funds have a rate of return of 10%/year, and income funds have a return of 6%/year. The growth, balanced, and income mutual funds are assigned risk factors of 0.1, 0.06, and 0.02, respectively. Sharon has decided that at least 50% of her total portfolio is to be in income funds and at least 25% of it in balanced funds. She has also decided that the average risk factor for her investment should not exceed 0.05. How much should Sharon invest in each type of fund in order to realize a maximum return on her investment? Hint: The constraint for the average risk factor for the investment is given by
0.1x + 0.06y + 0.02z ≤ 0.05(x + y + z).

growth funds ______ $
balanced funds ______ $
income funds ______ $

What is the maximum return?
$ __________