Calculating -R ymax from a given xmax and plot width

Dear List,

I'm trying to plot a Lambert Conformal Projection on it leaving a 5mm margin around it. I have a page of A4 paper in landscape orientation measuring 297mm x 210mm. After shifting the plot origin by +0.5c in x- & y-direction to get the left and lower margin, I use

-JLlon0/lat0/lat1/lat2/28.7c

to get the 5mm margin on the right side. To get the same margin at the upper border, I currently take a rough guess on the xmax and ymax values for -R...r and then tweaking these values until I get an eyeballed 5mm margin. This is not exact and becomes a really tedious task for charts at higher latitudes. 

Therefore I'm looking to automate this. My current thinking is to take my eyeballed -R xmax and calculate the required ymax value from xmax and the plot height of 200mm. I had a close look at mapproject -I, but my experimentation didn't yield anything useful so far. I have problems mixing the geodetical xmax with the Cartesian plot height.

Any input is greatly appreciated.

All the best,
Kristof

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