prologues:=2; 
beginfig(1);
u:=0.025cm;
pickup pencircle scaled 1;
pair origin,top_left,bottom_right;
origin=(320u,860u);
top_left=(320u,1060u);
bottom_right=(580u,860u);
path vert_axis,horiz_axis,budget_set;
vert_axis=origin--top_left;
draw vert_axis;
label.lft(btex $y$ etex,(320u,1060u));
label.bot(btex $x$ etex,(580u,860u));
label.llft(btex $0$ etex,origin);
horiz_axis= origin--bottom_right;
draw horiz_axis;
pair upper_left_budget_line,bottom_right_budget_line;
upper_left_budget_line=7/8[origin,top_left];
bottom_right_budget_line=3/4[origin,bottom_right];
draw upper_left_budget_line--bottom_right_budget_line;
label.lft(btex ${W}\over{p_y}$ etex,upper_left_budget_line);
label.bot(btex ${W}\over{p_x}$ etex,bottom_right_budget_line);
director:=angle(bottom_right_budget_line-upper_left_budget_line);
pair tangency,left_wing,right_wing;
tangency:=(1/2)[upper_left_budget_line,bottom_right_budget_line];
left_wing:=(-40u,90u);
right_wing:=(90u,-40u);
draw (tangency+left_wing)..(tangency+(2u,2u)){dir director}..(tangency+(25u,-15u))..(tangency+right_wing) withcolor green;
dotlabel.urt(btex $(x^\ast,y^\ast) $ etex,(tangency+(1u,1u)));
drawarrow tangency..(tangency-(0,15u));
drawarrow (tangency-(0,15u))--(tangency+(25u,-15u));
dotlabel.rt(btex $(x^\ast+dx,y^\ast-dy)$ etex,(tangency+(25u,-15u)));
endfig;
end