(*UNIVERSAL CONSTANTS*)
g0 =  9.81;(*~Earth surface gravity*)
G = 6.67430*10^-11;(*Gravitational Constant*)
(*PLANETARY VARIABLES*)
DPR = 6371000;(*Planet radius*)
MP=5.9722*(10^24);(*Planet mass*)
(*TRAJECTORY VARIABLES*)
DFH=120000; (*Final Height*)
DIH=0;(*Initial height*)
(*STRUCTURAL VARIABLES*)
MFT=5;(*Mass of full tank*)
MET=0.12;(*Mass of empty tank*)
MO=0;(*Additional mass (fairings, pipes,landing struts, etc)*)
p=5.2;(*payload*)
(*ENGINE VARIABLES*)
ME= 1;(*Engine mass*)
TET = 40;(*Engine Thrust in tonnes*)
ISP = 420;(*ISP*)
(*Situational variables*)
GS=1;(*Gravity switch*)
v = 7800; (*Desired v*)

f[x_, y_] := (g0*ISP*Log[(p + ((y/ME)*ME + MO) + (x/MFT)*MFT)/(p + ((y/ME)*ME + MO) + (x/MFT)*MET) ] - GS*(G*MP/(DFH - DIH)*Abs[1/(DPR + DFH) - 1/(DPR + DIH)])*((x/MFT)*(MFT - MET)/((y/ME)*TET/ISP)))

ENG=1;(*Number of engines*)
F=8;(*Number of fuel tanks*)
(g0*ISP*Log[(p + ((ENG/ME)*ME + MO) + (F/MFT)*MFT)/(p + ((ENG/ME)*ME + MO) + (F/MFT)*MET) ] - GS*(G*MP/(DFH - DIH)*Abs[1/(DPR + DFH) - 1/(DPR + DIH)])*((F/MFT)*(MFT - MET)/((ENG/ME)*TET/ISP)))

Show[
  Plot3D[f[x, y], {x, 0, 400*MFT}, {y, 0, 20*ME},
    PlotRange -> {0, 20000},
    Mesh -> None,
    ColorFunction -> "Rainbow",
    PlotPoints -> 50
  ],
  Plot3D[v, {x, 0, 400*MFT}, {y, 0, 20*ME},
    Mesh -> None,
    PlotStyle -> Directive[Opacity[0.3], Red]
  ]
]

contourPlot = ContourPlot[
  f[x, y] == v,
  {x, MFT, 400*MFT},
  {y, ME, 20*ME},
  ContourShading -> False,
  Contours -> {v},
  FrameLabel -> {"Mass of fuel tanks", "Mass of Engines"}
]

data = Table[
  {x, y, f[x, y]},
  {x, MFT, 400*MFT, MFT},
  {y, ME, 20*ME, ME}  (* start from mass to avoid division by zero *)
];

flattenedData = Flatten[data, 1];  (* Flatten to list of {x, y, z} *)

tolerance = 25;  (* how close to v in m/s*)

filteredPoints = Select[
  flattenedData,
  #[[3]] > v &
];

MinPoint = MinimalBy[filteredPoints, #[[1]] + #[[2]] &][[1]] ;
{xMin, yMin, fVal} = MinPoint;
wMin = xMin + yMin +p+MO;
Ms=xMin + yMin + MO;
nF=xMin/MFT;
nE=yMin/ME;
ve=fVal-v;
 wMin
 " is the total mass"
Ms
" is the stage's mass"
nE
" is the number of engines"
nF
" is the number of fuel tanks"
ve
" is the extra speed"