Question: Ludwigshöhe is situated near which highest peak of Monte Rosa?

Context paragraphs:
Monte Rosa (disambiguation): Monte Rosa, or Monte Rosa Massif, is a mountain massif of the Alps.  The massif's highest mountain is sometimes called Monte Rosa.

MS Monte Rosa: Several motor ships have borne the name Monte Rosa after Monte Rosa, the highest mountain in Switzerland:

Dufourspitze: The Dufourspitze is the highest peak of Monte Rosa, a huge ice-covered mountain massif in the Alps.  Dufourspitze is the highest mountain peak of both Switzerland and the Pennine Alps and is also the second-highest mountain of the Alps and Europe outside the Caucasus.  It is located between Switzerland (Canton of Valais) and Italy (Piedmont and Aosta Valley).

Monte Rosa Hut: The Monte Rosa Hut (German: "Monte Rosa Hütte" ) is a mountain hut located near Zermatt on the Monte Rosa massif (up to 4634 m ) and above the Grenzgletscher (Border Glacier) sitting on a glacier-free rocky part called "Untere Plattje" at an altitude of 2883 m .  It is owned by the Swiss Alpine Club SAC.  The hut is the start of the normal route to the summit and other mountains in the area.  The first hut was built in 1894–1895 just next to the then still much higher Border Glacier at an altitude of 2795 m .  A completely new building was inaugurated in 2009, a hi-tech, energy-wise almost self-sufficient, environmentally friendly mountain hut based on wood with an aluminum shell.

Dunantspitze: The Dunantspitze (German for "Peak Dunant", 4,632 m), formerly called Ostspitze ("Eastern Peak"), is a peak of the Monte Rosa Massif in the Pennine Alps in Switzerland.  It is the second highest peak of the massif, after the Dufourspitze (4,634 m) and the second highest summit in Switzerland, but its prominence is only about 15 metres.  At the time of its first ascent it was unclear which of the summits was the higher.

Monte Rosa: The Monte Rosa (or synonymously used as a pleonasm: "Monte Rosa massif" (Italian: "massiccio del Monte Rosa" ; German: "Monte Rosa-Massiv" ; French: "massif du Mont Rose" ) is a mountain massif located in the eastern part of the Pennine Alps.  It is located between Switzerland (Valais) and Italy (Piedmont and Aosta Valley).  Monte Rosa is the second highest mountain in the Alps and western Europe.

Institut Monte Rosa: Institut Monte Rosa, commonly referred to as Monte Rosa or Monte, is a private, international boarding school, in Territet near Montreux, Switzerland.

Lysjoch: The Lysjoch (or Lisjoch) (French: "Col du Lys" , Italian: "Colle del Lys" ) is a very high pass in the Pennine Alps between Italy and Switzerland.  It is located east of the Lyskamm and west of the Ludwigshöhe near Monte Rosa.  The pass is at 4,151 meters and is east of the Entdeckungsfels.

Ludwigshöhe (mountain): The Ludwigshöhe is a mountain in the Pennine Alps on the Swiss-Italian border.  It is situated near the Dufourspitze in the Monte Rosa Massif.  The summit is the tripoint between Valais, Aosta Valley and Piedmont.

Monte Rosa Hotel: The Monte Rosa is a hotel, located in the main street of Zermatt.  It was frequented by the members of the Alpine Club, including Edward Whymper who made the first ascent of the Matterhorn in 1865.  The hotel is named after the highest mountain near Zermatt, Monte Rosa.

Supporting paragraphs: Ludwigshöhe (mountain) Dufourspitze
Answer: Dufourspitze