Fig2_121.html

restart; -1

dydx1 := diff(y, x1); 1

`+`(`-`(`*`(`/`(1, 50), `*`(x1))), 144, `-`(`*`(`/`(7, 1000), `*`(x2))))

dydx2 := diff(y, x2); 1

`+`(`-`(`*`(`/`(7, 1000), `*`(x1))), `-`(`*`(`/`(1, 50), `*`(x2))), 174)

s := solve({dydx1 = lambda, dydx2 = lambda, `+`(x1, x2) = 10000}, {lambda, x1, x2}); 1

{lambda = 24, x1 = `/`(50000, 13), x2 = `/`(80000, 13)}

evalf(s)

{lambda = 24., x1 = 3846.153846, x2 = 6153.846154}

evalf(eval(y, s))

532307.6923

with(plots); -1

a := contourplot(y, x1 = 0 .. 10000, x2 = 0 .. 10000, axes = boxed, color = black, contours = [0, 100000, 200000, 300000, 400000, 500000, 532308]); -1

a := contourplot(y, x1 = 0 .. 10000, x2 = 0 .. 10000, axes = boxed, color = black, contours = [0, 100000, 200000, 300000, 400000, 500000, 532308]); -1

b := implicitplot({x1 = 5000, x2 = 8000, `+`(x1, x2) = 10000}, x1 = 0 .. 10000, x2 = 0 .. 10000, axes = boxed, color = red); -1

b := implicitplot({x1 = 5000, x2 = 8000, `+`(x1, x2) = 10000}, x1 = 0 .. 10000, x2 = 0 .. 10000, axes = boxed, color = red); -1

display({a, b}); 1

Plot_2d

plot3d(y, x1 = -100000000 .. 100000000, x2 = -100000000 .. 100000000)

Plot_2d

s1 := solve({dydx1 = lambda, dydx2 = lambda, x1 = 5000}, {lambda, x1, x2}); 1

{lambda = -`/`(93, 13), x1 = 5000, x2 = `/`(95000, 13)}

evalf(s1)

{lambda = -7.153846154, x1 = 5000., x2 = 7307.692308}

s2 := solve({dydx1 = lambda, dydx2 = lambda, x2 = 8000}, {lambda, x1, x2}); 1

{lambda = -`/`(336, 13), x1 = `/`(74000, 13), x2 = 8000}

evalf(s2)

{lambda = -25.84615385, x1 = 5692.307692, x2 = 8000.}

s3 := solve({dydx1 = lambda, dydx2 = lambda, x1 = 0}, {lambda, x1, x2}); 1

{lambda = `/`(1662, 13), x1 = 0, x2 = `/`(30000, 13)}

evalf(s3)

{lambda = 127.8461538, x1 = 0., x2 = 2307.692308}

evalf(eval(y, s3))

s4 := solve({dydx1 = lambda, dydx2 = lambda, x2 = 0}, {lambda, x1, x2}); 1

{lambda = `/`(2472, 13), x1 = -`/`(30000, 13), x2 = 0}

evalf(s4)

{lambda = 190.1538462, x1 = -2307.692308, x2 = 0.}

`%%%%%%%%%%%%%%%%%%%%%`

evalf(eval(y, {x1 = 0, x2 = 8000}))

352000.

evalf(eval(y, {x1 = 5000, x2 = 0}))

70000.

evalf(eval(y, {x1 = 2000, x2 = 8000}))

488000.

evalf(eval(y, {x1 = 8000, x2 = 2000}))

308000.