the example given is correctly stated by Two_squirrels, with a little more detail provided: The zero-NM payload is calculated by starting with the HOGE weight at the stated condition (the Marine Hot Day, 3000 feet, 31.5 degrees C) and then subtracting the equipped empty weight of the aircraft, all required mission equipment, the crew, the reserve fuel (usually 10% or 20 min, whichever is more). This is the max payload - the weight the aircraft can carry at HOGE with if it had only reserve fuel on board.
Then the fuel to fly out 110 miles (loaded) and back 110 miles (unloaded) is subtracted from the max payload, leaving 27,000 lbs.
To plot this on a Payload-Radius curve, place the max zero NM weight on the far left as the max value, along the upper left side. Then decrement the payload for each mile of fuel burned. Just take fuel flow and divide by TAS at best range speed - for the 53K, a guess might be about 28 lbs per mile range - 56 lb/mile radius (4000lbs/hr divided by 140 NM/hr = 28 Lb/NM). This means the 53K would pick up 34000 lb at zero miles, and 27,000 lbs at 110 miles.