An investor has 75,000 to invest in a CD and a mutual fund. The CD yields 6​% and the mutual fund yields 8%. The mutual fund requires a minimum investment of $8,000​, and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the​ return? What is the maximum​return?

Answer:investment in cd = x  = $50000investment in mutual funds  = $ 25000return = $5000Step-by-step explanation:let x be the investment in CDlet y be in mutual fundfrom the data given we haveReturn  = 6% x + 8% yReturn = 0.06 x + 0.08 y[tex]y \geq  8000[/tex][tex]x \geq 2y[/tex][tex]x + y \leq 7500[/tex]plotting these three inequalities on graph  we have critical number as(16000, 8000) : return = 0.06 (16000 + 0.08 (8000) = $1600(50000, 25000) : return = 0.06 (50000) + 0.08 (25000) = $5000(67000, 8000) return = 0.06 (67000) + 0.08(8000) = $4660As we can see maximum benefit is $5000 so we have investment in cd = x  = $50000investment in mutual funds  = $ 25000return = $5000