A Boeing 737 Max is displayed during the Farnborough Airshow, in Farnborough, on July 18, 2022. (Photo by JUSTIN TALLIS / AFP) (Photo by JUSTIN TALLIS/AFP via Getty Images)Justin Tallis | AFP | Getty ImagesBoeing handed over 60 new aircraft last month, the most since March, as the manufacturer tries to ramp up production of some of its bestselling planes.So far this year, Boeing delivered 266 aircraft to customers, shy of the 316 rival Airbus has handed over. Both manufacturers have struggled to increase output fast enough to avoid delays to airline customers eager for more planes during a boom in air travel.Boeing said Tuesday it logged orders for 288 aircraft, net of cancellations and conversions, in June, most of them from the massive order Air India announced earlier this year and firmed up at the Paris Air Show last month. The 470-jet order was split between Boeing and Airbus. Boeing’s June tally included nearly 40 787 Dreamliners for new Saudi carrier Riyadh Air, part of a deal announced in March.Boeing’s total net orders for the month came in at 305 aircraft after it added some planes to its backlog. The company routinely removes or adds planes to its backlog for reasons including whether a customer is likely to have financing to buy the aircraft.Boeing is scheduled to report second-quarter results on July 26, when it will update investors on its plans to increase production of its 737 Max planes and 787 Dreamliners.