8 : Alberta has a total of $ 200,000 to invest in three types of mutual funds: growth, balanced, and income funds. Growth funds have a rate of return of 12% per year, balanced funds have a rate of return of 10% per year, and income funds have a return of 6% per year. The growth, balanced, and income funds are assigned risk factors of 0.1, 0.06, and 0.02, respectively. Alberta has decided that at least 50% of her total portfolio is to be in income funds and at least 10% in balanced funds. She has also decided that the average risk factor for her investment should not exceed 0.05. How should Alberta allocate her funds so as to maximize the 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) 0.1 x + 0.06 y + 0.02 z ≤ 0.05 ( x + y + z ) .) growth balanced income $ 50000.0 $ 50000.0 $ 100000.0