Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.1;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.12;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.14;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.16;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.17;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.18;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.19;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.2;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.21;
m=10;
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]

Clear[NInput,PInput,sink,f,r,m,k,q,α,Nit,P,x,y];
NInput=.2;
PInput=0.004;
sink=.01;
f=0.88;
r=.22;
m=10;21
k=30.0;
q=2.0;
α=0.2;
NSolve[NInput-sink*x+f*y*((E^(-α*(x/y -k)))/(1+(E^(-α*(x/y -k)))))==0&&PInput-sink*y+((r*y^q)/(m^q+y^q))==0,{x,y},Reals]