Which company beginning with i created r-type?

The name of the company who produced R-Type and its sequel its sequels is Irem. They launched the game in 1987.

Founded in 1974 as IPM, the company changed its name in 1979 to Irem, which stands for Innovations in Recreational Electronic Media. Their first big arcade hit was Moon Patrol in 1982. These days, the company produces games solely for PlayStation.

R-Type - The Essential Arcade Game of the Late 1980s

Irem is still most famous for the R-Type series of games and the original game ported onto almost every games console there was at the time. R-Type heralded a new age in the horizontal scroller shoot-em-up and as well as sequels, spawned a number of copycat games, such as Pulstar and Salamander.

The 'final' R-Type game was released in 2003 by Irem for the PlayStation.

This YouTube user has his own original R-Type arcade game: