No. of constraints =

integer solution

(1):

(2):

(3):

(4):

(5):

(6):

f(x,y) =

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feasible region

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grid lines

c6(x, y) = x + y > 6
c5(x, y) = y ≥ 0
c4(x, y) = x ≥ 0
listNum: {3, 4, 5, 6}
n: SelectedIndex[listNum] + 2
c3(x, y) = (6 * x) + (10 * y) ≤ 900
c2(x, y) = (1.2 * x) ≤ 90
c1(x, y) = (4 * x) + (20 * y) ≤ 1400
sol = If(n ≟ 6, c1(x, y) ∧ c2(x, y) ∧ c3(x, y) ∧ c4(x, y) ∧ c5(x, y) ∧ c6(x, y), If[n ≟ 5, c1(x, y) ∧ c2(x, y) ∧ c3(x, y) ∧ c4(x, y) ∧ c5(x, y), If[n ≟ 4, c1(x, y) ∧ c2(x, y) ∧ c3(x, y) ∧ c4(x, y), If[n ≟ 3, c1(x, y) ∧ c2(x, y) ∧ c3(x, y)]]])
showInt = true
inputBox1 = Textfield(c1)
inputBox2 = Textfield(c2)
inputBox3 = Textfield(c3)
inputBox4 = Textfield(c4)
inputBox5 = Textfield(c5)
inputBox6 = Textfield(c6)
f(x, y) = (10 * x) + (30 * y)
inputBoxFunction = Textfield(f)
P = PointIn(sol)
s1 = true
s2 = true
s3 = true
s4 = true
s5 = true
s6 = false
showP = true
showSol = true
listVertex = RemoveUndefined({Vertex[sol]})
maxX: ceil(Max[Sequence[x(Element[listVertex, i]), i, 1, Length[listVertex]]])
maxY: ceil(Max[Sequence[y(Element[listVertex, i]), i, 1, Length[listVertex]]])
minX: floor(Min[Sequence[x(Element[listVertex, i]), i, 1, Length[listVertex]]])
minY: floor(Min[Sequence[y(Element[listVertex, i]), i, 1, Length[listVertex]]])
text1a: "f(x,y)=" + (LaTeX[f]) + "\\f" + (LaTeX[P]) + "=" + (LaTeX[f(P)]) + ""
L = ImplicitCurve(f(x, y) - f(x(P), y(P)))
showLine = true
showGrid = false
text3: "\[\left\{\begin{array}{rcl}" + (LaTeX[c1]) + " \\" + (LaTeX[c2]) + "  \\" + (LaTeX[c3]) + "\end{array}\right.\]"
text4: "\[\left\{\begin{array}{rcl}  " + (LaTeX[c1]) + "\\   " + (LaTeX[c2]) + "\\ " + (LaTeX[c3]) + "\\" + (LaTeX[c4]) + "\end{array}\right.\]"
text5: "\[\left\{\begin{array}{rcl}  " + (LaTeX[c1]) + "\\   " + (LaTeX[c2]) + "\\ " + (LaTeX[c3]) + "\\" + (LaTeX[c4]) + "\\" + (LaTeX[c5]) + "\end{array}\right.\]"
text6: "\[\left\{\begin{array}{rcl}  " + (LaTeX[c1]) + "\\   " + (LaTeX[c2]) + "\\ " + (LaTeX[c3]) + "\\" + (LaTeX[c4]) + "\\" + (LaTeX[c5]) + "\\" + (LaTeX[c6]) + " \end{array}\right.\]"
opacity = 0.25
text1b: "" + (LaTeX[L]) + ""
Q = Intersect(L, yAxis)
a: 1 - s4
b: 1 - s5
c: 1 - s6