How to find the maximum income? (See picture)Thanks!

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Answer 1 · 2018-02-05T20:34:45

See below.

Calling

#x_1 = # amount invested in stable bonds
#x_2 = # amount invested in volatile bonds

#c_1 = # unit profit for stable bonds
#c_2 = # unit profit for volatile bonds

we have the optimization problem

#max f = c_1 x_1+c_2 x_2#

subjected to

#40000 le x_1#
#0 le x_2 le 60000#
#x_1+x_2 le 130000#
#x_1 le x_2#

The feasible region as well as the maximization condition can be depicted in the attached figure.

The result is

#x_1 = x_2 = 60000# giving a profit of #9900#

enter image source here