Question 1190768
x = 2% investment
y = 5% investment


constraints are:
x >= 10
y <= 20
x + y <= 40
x >= 0
y >= 0
objective function is:
profit = .02x + .05y


using the desmos.com calculator, you would:
graph the opposite of the inequalities.
the area of the graph that is not shaded is you region of feasibility.
the corner points of the region of feasibility are where yoour maximum solution lies.
evaluate the objective function at each of these corner point.


this is what the graph looks like:


<img src = "http://theo.x10hosting.com/2022/021201.jpg" >


your corner points are:
(10,0)
(10,20)
(20,20)
(40,0)


at (10,0), the profit is .02 * 10 + .05 * 0 = .2 * 1000 = 200
at (10,20), the profit is .02 * 10 + .05 * 20 = 1.2 * 1000 = 1200
at (20,20), the profit is  .02 * 20 + .05 * 20 = 1.4 * 1000 = 1400
at (40,0), the profit is .02 * 40 + .05 * 0 = .8 * 1000 = 800


your maximum profit is when x = 20 and y = 20.
that would be 20,000 invested in account A and 20,000 invested in account B.
.02 * 20,000 + .05 * 20,000 = 1400.


all your constraints need to be satisfied at that corner point.


at (20,20):
x >= 10 is satisfied.
y <= 20 is satisfied.
x + y <= 40 is satisfied.
x >= 0 is satisfied.
y >= 0 is satisfied.


let me know if you have any questions.