Ethan Windsor & Lauren PrewMinimize the Surface Area of a BoxMath 152 - Section 201restart:with(Maplets[Tools]): with(Maplets[Elements]):StartEngine();randomize():lightorange:="#FFB300":
lightcyan:="#DDFFFF":ColorFooter:=lightcyan:
FontFooter:=Font("helvetica",10):randL:=rand(1..10):problem:=proc()
global areaw, mwid, mhgt;
local vol, hgt, plotlist, plotlist2, R, canplot;
areaw:=w^2+4*vol/w;
mwid:=2*randL();
vol:=mwid^3/2;
Set(mliter=vol);
mhgt:=mwid/2;
Set(TFarea="");
Set(TFvolume="");
Set(TFareaw="");
Set(TFmwid="");
Set(TFmhgt="");
Set(reply="");
end proc:hint1:=proc()
Set(reply="Add the area of the base and the area of the sides."):
end proc:check1:=proc()
local user_area;
if Get(TFarea)="" then
Set(reply="No answer given.");
return;
end if;
user_area:=Get(TFarea::anything):
if simplify(4*w*h+w^2 - user_area)=0 then
Set(reply="Correct."):
else
Set(reply="Incorrect."):
end if;
end proc:show1:=proc()
Set(TFarea="w^2+4*w*h"):
end proc:hint2:=proc()
Set(reply="Multiply the area of the base by the height."):
end proc:check2:=proc()
local user_volume;
if Get(TFvolume)="" then
Set(reply="No answer given.");
return;
end if;
user_volume:=Get(TFvolume::anything):
if simplify(w^2*h - user_volume)=0 then
Set(reply="Correct."):
else
Set(reply="Incorrect."):
end if;
end proc:show2:=proc()
Set(TFvolume="w^2*h"):
end proc:hint3:=proc()
Set(reply="Use the volume constraint to eliminate the variable h."):
end proc:check3:=proc()
global areaw;
local user_areaw;
if Get(TFareaw)=""then
Set(reply="No answer given.");
return;
end if;
user_areaw:=Get(TFareaw::anything):
if simplify(areaw - user_areaw=0) then
Set(reply="Correct."):
else
Set(reply="Incorrect."):
end if;
end proc:show3:=proc()
global areaw;
Set(TFareaw=areaw):
end proc:hint4:=proc()
Set(reply="Find the minimum width by setting the derivative of the surface area equal to zero."):
end proc:check4:=proc()
global mwid;
local user_mwid;
if Get(TFmwid)="" then
Set(reply="No answer given.");
return;
end if;
user_mwid:=Get(TFmwid::anything):
if simplify(mwid - user_mwid=0) then
Set(reply="Correct."):
else
Set(reply="Incorrect."):
end if;
end proc:show4:=proc()
global mwid;
Set(TFmwid=mwid):
end proc:hint5:=proc()
Set(reply="Plug the minimum width into the volume constraint."):
end proc:check5:=proc()
global mhgt;
local user_mhgt;
if Get(TFmhgt)="" then
Set (reply="No answer given.");
return;
end if;
user_mhgt:=Get(TFmhgt::anything):
if simplify(mhgt - user_mhgt=0) then
Set (reply="Correct."):
else
Set (reply="Incorrect."):
end if;
end proc:show5:=proc()
global mhgt;
Set(TFmhgt=simplify(mhgt)):
end proc:MinAreaBox:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN](title="Minimize the Surface Area of a Box",
[ halign=none,
[ Button("New Problem", Evaluate(function=problem), background=magenta),
HorizontalGlue(),
Button("Quit", Shutdown(), background=pink)
],
[ "A box with a square base, open top, and volume V =",
TextField[mliter](width=6,editable=false, background=white),
"cm^3 is being constructed.",
HorizontalGlue()
],
[ "Determine the dimensions (height h and width w) of the box with minimum surface area.",
HorizontalGlue()
],
[ border=true,
caption="Enter the Formula for the Surface Area of a box with a square base:",
"A =",
TextField[TFarea](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="Enter the Formula for the Volume of a box with a square base:",
"V =",
TextField[TFvolume](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="Express the Surface Area in terms of w:",
"A =",
TextField[TFareaw](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="Find the w which gives Minimum Area:",
"w =",
TextField[TFmwid](width=17, background=turquoise),
"cm",
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="Find the h which gives Minimum Area:",
"h =",
TextField[TFmhgt](width=17, background=turquoise),
"cm",
HorizontalGlue(),
Button("Hint", Evaluate(function="hint5"), background=lightorange),
Button("Check", Evaluate(function="check5"), background=green),
Button("Show", Evaluate(function="show5"), background=lightorange)
],
[ halign=none,
TextField[reply](width=40, editable=false, background=white)
],
[ halign=none, background=ColorFooter,
Label("Programmers: Ethan Windsor & Lauren Prew", font=FontFooter),
HorizontalGlue(),
Label("Copyright: P. Yasskin 2008", font=FontFooter)
]
]
)
):Maplets[Display]( MinAreaBox );