Brad Beless & Morgan VanDerLeestMATH 152-202Maplet Project - Maximizing Area Within a Fencerestart:with(Maplets[Tools]): with(Maplets[Elements]): with(plots):
StartEngine();randomize():lightorange:="#FFB300":
lightcyan:="#DDFFFF":ColorFooter:=lightcyan:
FontFooter:=Font("helvetica",10):problem:=proc()
global perimeter, Pens, comp_yofx, comp_Area, comp_Areap, comp_x, comp_y, comp_Amax;
local npens, P, numb_pens, fieldp, fencep, line1p, line2p, line3p, line4p, line5p, fence2, fence3, fence4, fence5, fence6, perim, outer, n;
perim:=rand(3..20);
outer:=perim();
npens:=rand(2..6);
numb_pens:=npens();
P:=(numb_pens)*outer;
Set(perimeter=P);
Set(Pens=numb_pens);
n:=numb_pens;
comp_yofx:=(P-(n+1)*x)/2;
comp_Area:=(P*x-(n+1)*x^2)/2;
comp_Areap:=(P-2*(n+1)*x)/2;
comp_x:=P/(2*(n+1));
comp_y:=P/4;
comp_Amax:=P^2/(4*(2*n+2));
fieldp:=plot([[-1,-1],[9,-1],[9,7],[-1,7],[-1,-1]], thickness=3, color=green, filled=true):
fencep:=plot([[0,0],[8,0],[8,6],[0,6],[0,0]], thickness=3, color=brown):
line1p:=plot([[0,1],[8,1]],thickness=3,color=brown):
line2p:=plot([[0,2],[8,2]],thickness=3,color=brown):
line3p:=plot([[0,3],[8,3]],thickness=3,color=brown):
line4p:=plot([[0,4],[8,4]],thickness=3,color=brown):
line5p:=plot([[0,5],[8,5]],thickness=3,color=brown):
fence2:=display(fieldp,fencep,line3p,axes=none):
fence3:=display(fieldp,fencep,line2p,line4p,axes=none):
fence4:=display(fieldp,fencep,line2p,line3p,line4p,axes=none):
fence5:=display(fieldp,fencep,line1p,line2p,line3p,line4p,axes=none):
fence6:=display(fieldp,fencep,line1p,line2p,line3p,line4p,line5p,axes=none):
if (numb_pens)=2 then
Set(FencePlot=fence2);
end if;
if (numb_pens)=3 then
Set(FencePlot=fence3);
end if;
if (numb_pens)=4 then
Set(FencePlot=fence4);
end if;
if (numb_pens)=5 then
Set(FencePlot=fence5);
end if;
if (numb_pens)=6 then
Set(FencePlot=fence6);
end if;
Set(TFyofx=""):
Set(TFArea=""):
Set(TFAreap=""):
Set(TFx=""):
Set(TFy=""):
Set(TFAmax=""):
Set(reply=""):
end proc:hint1:=proc()
Set(reply="Use the parameter formula ( P = (n+1)x + 2y ) and solve for y."):
end proc:check1:=proc()
global comp_yofx;
local user_yofx;
if Get(TFyofx)="" then
Set(reply="An answer is required.");
return;
end if;
user_yofx:=Get(TFyofx::anything):
if simplify(comp_yofx-user_yofx)=0 then
Set(reply="Excellent!"):
else
Set(reply="Try again."):
end if;
end proc:show1:=proc()
global comp_yofx;
Set(TFyofx=comp_yofx):
end proc:hint2:=proc()
Set(reply="Plug y-expression into the general formula for area ( A = x * y )."):
end proc:check2:=proc()
global comp_Area;
local user_Area;
if Get(TFArea)="" then
Set(reply="Try answering the problem before checking it.");
return;
end if;
user_Area:=Get(TFArea::algebraic):
if simplify(comp_Area - user_Area)=0 then
Set(reply="Nice job."):
else
Set(reply="It's not rocket science. Try again."):
end if;
end proc:show2:=proc()
Set(TFArea=comp_Area):
end proc:hint3:=proc()
Set(reply="Find derivative. You should know how to do that..."):
end proc:check3:=proc()
global comp_Areap;
local user_Areap;
if Get(TFAreap)=""then
Set(reply="Seriously? Checking comes after answering...");
return;
end if;
user_Areap:=Get(TFAreap::anything):
if simplify( comp_Areap - user_Areap)=0 then
Set(reply="Good work."):
else
Set(reply="Ooo. Close. But wrong."):
end if;
end proc:show3:=proc()
Set(TFAreap=comp_Areap):
end proc:hint4:=proc()
Set(reply="Set derivative found equal to zero and solve for x."):
end proc:check4:=proc()
global comp_x;
local user_x;
if Get(TFx)="" then
Set(reply="An answer would be nice.");
return;
end if;
user_x:=Get(TFx::anything):
if simplify(comp_x - user_x=0) then
Set(reply="Bravo!"):
else
Set(reply="That's a negatory. Give it another go."):
end if;
end proc:show4:=proc()
global comp_x;
Set(TFx=comp_x):
end proc:hint5:=proc()
Set(reply="Plug x-value from Question 4 into your original y(x) function."):
end proc:check5:=proc()
global comp_y;
local user_y;
if Get(TFy)="" then
Set (reply="Wouldn't you like to answer first?");
return;
end if;
user_y:=Get(TFy::anything):
if simplify(comp_y - user_y)=0 then
Set (reply="Whoop!"):
else
Set (reply="Ugh. No."):
end if;
end proc:show5:=proc()
global comp_y;
Set(TFy=comp_y):
end proc:hint6:=proc()
Set(reply="Use numerical values of x and y and plug them into the area formula."):
end proc:check6:=proc()
global comp_Amax;
local user_Amax;
if Get(TFAmax)="" then
Set (reply="It hardly seems fair to make me read your mind...");
return;
end if;
user_Amax:=Get(TFAmax::anything):
if simplify(comp_Amax - user_Amax)=0 then
Set (reply="Great!"):
else
Set (reply="I don't think so. In fact, I know it's not so."):
end if;
end proc:show6:=proc()
global comp_Amax;
Set(TFAmax=comp_Amax):
end proc:MaxFencedArea:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN](title="Maximizing Area Within a Fence",
[ [ Button("New Problem", Evaluate(function=problem), background=magenta),
HorizontalGlue(),
Button("Quit", Shutdown(), background=pink)
],
[ border=true,
"You are given",
TextField[perimeter](width=6, editable=false, background=white),
"ft of fence. Find the maximum fenced area if you must enclose",
TextField[Pens] (width=6, editable=false, background=white),
" pens."
],
[ halign=none, inset=0, spacing=0,
[ halign=none, inset=0, spacing=0,
[ border=true,
caption="Find the formula for y in terms of x:",
"y(x) =",
TextField[TFyofx](width=17, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint1"), background=lightorange),
Button("Check", Evaluate(function="check1"), background=green),
Button("Show", Evaluate(function="show1"), background=lightorange)
],
[ border=true,
caption="Find the general area in terms of x:",
"A =",
TextField[TFArea](width=17, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint2"), background=lightorange),
Button("Check", Evaluate(function="check2"), background=green),
Button("Show", Evaluate(function="show2"), background=lightorange)
],
[ border=true,
caption="Find the derivative of the area:",
"A' =",
TextField[TFAreap](width=17, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint3"), background=lightorange),
Button("Check", Evaluate(function="check3"), background=green),
Button("Show", Evaluate(function="show3"), background=lightorange)
],
[ border=true,
caption="Solve for x:",
"x =",
TextField[TFx](width=17, background=turquoise),
"ft",
HorizontalGlue(),
Button("Hint", Evaluate(function="hint4"), background=lightorange),
Button("Check", Evaluate(function="check4"), background=green),
Button("Show", Evaluate(function="show4"), background=lightorange)
],
[ border=true,
caption="Solve for y:",
"y =",
TextField[TFy](width=17, background=turquoise),
"ft",
HorizontalGlue(),
Button("Hint", Evaluate(function="hint5"), background=lightorange),
Button("Check", Evaluate(function="check5"), background=green),
Button("Show", Evaluate(function="show5"), background=lightorange)
],
[ border=true,
caption="Find the maximum area:",
"Amax =",
TextField[TFAmax](width=17, background=turquoise),
"ft",
HorizontalGlue(),
Button("Hint", Evaluate(function="hint6"), background=lightorange),
Button("Check", Evaluate(function="check6"), background=green),
Button("Show", Evaluate(function="show6"), background=lightorange)
]
],
[ border=true,
caption="The Fences:",
Plotter[FencePlot](width=200, height=200)
]
],
[ halign=none,
TextField[reply](width=65, editable=false, background=white)
],
[ halign=none, background=ColorFooter,
Label("Programmers: Brad Beless & Morgan VanDerLeest", font=FontFooter),
HorizontalGlue(),
Label("Copyright: P. Yasskin 2008", font=FontFooter)
]
]
)
):Maplets[Display]( MaxFencedArea );