Answer:
(2, 0)
Step-by-step explanation:
To solve this problem, we have to plot a graph. A graph was plotted using geogebra online graphing calculator. From the attached graph we can see the points that satisfy the constraints: (0,0), (2, 0), (2, 6), (6, 4). But since x,y > 0, this leaves us with B(2, 6), C(2, 0), D(6, 4)
The cost equation is C = 3x + 4y
At point B(2, 6): C = 3(2) + 4(6) = 30
At point C(2, 0): C = 3(2) + 4(0) = 6
At point D(6, 4): C = 3(6) + 4(4) = 34
Therefore the minimum cost is at C(2, 0)
Substituting this into the other ODE gives
Since , it follows that
. The ODE in
has characteristic equation
with roots , admitting the characteristic solution
From the initial conditions we get
So we have
Take the derivative and multiply it by -1/4 to get the solution for :