Food distributor Sysco Corp and its biggest rival, US Foods Inc , have offered to sell a smaller competitor 11 facilities in order to convince skeptical antitrust regulators to approve their $3.5 billion merger, a source briefed on the matter told Reuters. The deal, proposed in December 2013, is seen as problematic because Sysco and US Foods are the only companies with the geographic reach to offer nationwide contracts to deliver a wide range of goods to customers ranging from hotel chains to hospitals to fast food chains and fine restaurants.