Homework Sourseplease fill in the three missing boxesSolutionTotal 35 mill
please fill in the three missing boxes.
Solution
Total = $35 million
treaaury bonds rate = 6% annual interest, initial fee = $100 per million
mutual funds rate = 8% , initial fee = $200 per million
let treasury bonds and mutual fund investment is x and y million respectively
then fees will be $100x and $200y respectively
so 100x +200y <= 6000 => 6000 - 100x -200y >=0 -----------------------------------(1)
the x >= $5 => x-5 =>0--------------------------------(2)
y >= $15 =>y-15 =>0 ---------------------------------(3)
annual interest is I = 0.06x +0.08y ---------------------------------------(4)
need tp maximize I constrained to (1), (2), (3)
let L(x,y) = I + k{(x-5)+(y-15)+(6000 - 100x -200y)}
= 0.06x +0.08y + k{(x-5)+(y-15)+(6000 - 100x -200y)}
partially differentaiting L(x,y) wrt x and y
Lx = 0.06 +k(-99)
