Imagemagick: convert TIF image to EPS keeping resolution - imagemagick

Question

I have been trying to convert an tif image to an eps image keeping the original resolution for days. But without success. The problem is that imagemagick always sets the resolution of the eps image to 72 dpi regardless of using the density and resize command before or after the input file.
The input file can be downloaded, for example I tried following imagemagick command (all of them without the desirable result):
convert -density 300 input.TIF -profile "ISOcoated_v2_eci.icc" eps3:output.EPS
convert -density 300 input.TIF -profile "ISOcoated_v2_eci.icc" -geometry 2835x3780 eps3:output.eps
convert -density 300 input.TIF -profile "ISOcoated_v2_eci.icc" -resize 2835x3780 eps3:output.eps
What is wrong on my conversion? I just need an output eps image with the the resolution of 300 dpi as the input tif file.
Added: identify of output.eps
Image: output.eps
Format: PAM (Common 2-dimensional bitmap format)
Mime type: image/x-portable-pixmap
Class: DirectClass
Geometry: 680x907+0+0
Resolution: 72x72
Print size: 9.44444x12.5972
Units: Undefined
Type: ColorSeparation
Base type: ColorSeparation
Endianess: Undefined
Colorspace: CMYK
Depth: 16/8-bit
Channel depth:
cyan: 8-bit
magenta: 8-bit
yellow: 8-bit
black: 8-bit
Channel statistics:
Pixels: 616760
Cyan:
min: 0 (0)
max: 65535 (1)
mean: 8034.92 (0.122605)
standard deviation: 16075.5 (0.245296)
kurtosis: 3.34548
skewness: 2.18869
Magenta:
min: 0 (0)
max: 63993 (0.976471)
mean: 6431.6 (0.0981399)
standard deviation: 13251.7 (0.202209)
kurtosis: 4.41467
skewness: 2.36107
Yellow:
min: 0 (0)
max: 62965 (0.960784)
mean: 3296.53 (0.0503018)
standard deviation: 8665.27 (0.132224)
kurtosis: 11.9555
skewness: 3.37656
Black:
min: 0 (0)
max: 61166 (0.933333)
mean: 3413.91 (0.052093)
standard deviation: 10294.1 (0.157078)
kurtosis: 10.6052
skewness: 3.33169
Image statistics:
Overall:
min: 0 (0)
max: 65535 (1)
mean: 5294.24 (0.0807849)
standard deviation: 12400.4 (0.189219)
kurtosis: 7.42941
skewness: 2.89771
Total ink density: 324.706%
Rendering intent: Perceptual
Gamma: 0.454545
Chromaticity:
red primary: (0.64,0.33)
green primary: (0.3,0.6)
blue primary: (0.15,0.06)
white point: (0.3127,0.329)
Background color: cmyk(255,255,255,0)
Border color: cmyk(223,223,223,0)
Matte color: cmyk(189,189,189,0)
Transparent color: cmyk(0,0,0,0)
Interlace: None
Intensity: Undefined
Compose: Over
Page geometry: 680x907+0+0
Dispose: Undefined
Iterations: 0
Compression: Undefined
Orientation: Undefined
Properties:
date:create: 2015-09-09T10:21:04+02:00
date:modify: 2015-09-09T10:21:04+02:00
ps:HiResBoundingBox: 680.4x907.2+0+0
ps:Level: Adobe-3.0 EPSF-3.0
signature: 141246e610fe99f6d715095d32098b493a3258c58c755dd44cacb68b5be4129a
Artifacts:
filename: output.eps
verbose: true
Tainted: False
Filesize: 2.467MB
Number pixels: 617K
Pixels per second: 9.223372EB
User time: 0.000u
Elapsed time: 0:01.000
Version: ImageMagick 6.8.9-8 Q16 x64 2014-08-26 http://www.imagemagick.org
Added: identify of temp.png
Image: temp.png
Format: PNG (Portable Network Graphics)
Mime type: image/png
Class: DirectClass
Geometry: 2835x3780+0+0
Resolution: 300x300
Print size: 9.45x12.6
Units: Undefined
Type: TrueColor
Endianess: Undefined
Colorspace: sRGB
Depth: 16-bit
Channel depth:
red: 16-bit
green: 16-bit
blue: 16-bit
Channel statistics:
Pixels: 10716300
Red:
min: 0 (0)
max: 65535 (1)
mean: 56707.6 (0.865302)
standard deviation: 17939.1 (0.273732)
kurtosis: 3.27011
skewness: -2.18726
Green:
min: 771 (0.0117647)
max: 65535 (1)
mean: 57871 (0.883055)
standard deviation: 16384.1 (0.250006)
kurtosis: 3.99522
skewness: -2.33806
Blue:
min: 1419 (0.0216526)
max: 65535 (1)
mean: 60137.5 (0.91764)
standard deviation: 13808.7 (0.210707)
kurtosis: 6.52445
skewness: -2.76051
Image statistics:
Overall:
min: 0 (0)
max: 65535 (1)
mean: 58238.7 (0.888665)
standard deviation: 16134.1 (0.246191)
kurtosis: 4.60442
skewness: -2.44957
Rendering intent: Perceptual
Gamma: 0.45455
Chromaticity:
red primary: (0.64,0.33)
green primary: (0.3,0.6)
blue primary: (0.15,0.06)
white point: (0.3127,0.329)
Background color: white
Border color: srgb(223,223,223)
Matte color: grey74
Transparent color: black
Interlace: None
Intensity: Undefined
Compose: Over
Page geometry: 2835x3780+0+0
Dispose: Undefined
Iterations: 0
Compression: Zip
Orientation: Undefined
Properties:
date:create: 2015-09-09T10:16:17+02:00
date:modify: 2015-09-09T10:18:20+02:00
png:bKGD: chunk was found (see Background color, above)
png:cHRM: chunk was found (see Chromaticity, above)
png:gAMA: gamma=0.45454544 (See Gamma, above)
png:IHDR.bit-depth-orig: 16
png:IHDR.bit_depth: 16
png:IHDR.color-type-orig: 2
png:IHDR.color_type: 2 (Truecolor)
png:IHDR.interlace_method: 0 (Not interlaced)
png:IHDR.width,height: 2835, 3780
png:pHYs: x_res=300, y_res=300, units=0
png:sRGB: intent=0 (Perceptual Intent)
png:text: 4 tEXt/zTXt/iTXt chunks were found
ps:HiResBoundingBox: 680.4x907.2+0+0
ps:Level: Adobe-3.0 EPSF-3.0
signature: dffc47b2e7b1b0bdc1c8afe849bc84561743fe757c4ebb5093487547f67f2d9d
Artifacts:
filename: temp.png
verbose: true
Tainted: False
Filesize: 13.38MB
Number pixels: 10.72M
Pixels per second: 20.61MB
User time: 0.530u
Elapsed time: 0:01.520
Version: ImageMagick 6.8.9-8 Q16 x64 2014-08-26 http://www.imagemagick.org