Question

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Find and classify the equilibrium points of the following equations: C = (10 – 2x – 3y)x (6 – X – 2yly ў Discuss the stability of each equilibrium point.

Answer 1

A = 10-2x-31 (6-x-2y)y. To find equilibsicum (2 6-4 3 2 x 0 = y = 2 x = 6-29 = @ gives 6-4=2 ② gives points, let (10 -2x-3y) & too & (6-x-2y) y so Suppose ato, y to lo-22-3y =0 Ⓡ & x-2y gines. -2 tyzo (x,y) = (2, 2), Suppose azo, 4to. 6-x-2y=0 → 6-240 34-3 (aiy) = (0,3) Suppose ato, go 10- 2x-3y = 3 10-2x =0 (x,y) = (5,0) clegsly is also equilibrium point. Equilibrium points of given equations are co, o 2,(0,3), (5,0), (2,2). Now, to check the stability of these points, let f(x,y) = (10-2x-3y) a & groig) = (6-x-2y y gives - 2 = S (مرم)