Cutting a hundred million of a thirty-year bond down to fifty takes five hundred futures, and the usual arithmetic of fifty million over a hundred thousand lands there only because the contract's duration per dollar of face happens to match the bond's. What a hedge matches is dollars per basis point: 56,288.92 against 112.5778. Hold a thirty-year zero instead and the same job needs 1,234 contracts, while five hundred three-month contracts would cover 22.2 per cent of it.
Fourteen billion fill-ups a year divided by what a pump could do at full tilt gives 25,000 stations; divided by what a pump actually does it gives 149,829, inside the published range. The gap is exactly six, and the article proves that six is the ratio of the two throughput guesses alone, because the fleet, the fill-up frequency, the opening hours and the pumps per station all cancel. The utilisation of one sixth is Little's law read as 2.67 busy hours in a sixteen-hour day.
Two outlets in a town of fifty thousand is one per twenty-five thousand people, which scaled to the United States gives 13,600 against a published count near 13,500. That 0.74 per cent is luck, and the article shows why: the answer is exactly inversely proportional to the one density guess, and sweeping it across every defensible value spans 8,500 to 22,667. A second chain built from revenue, sharing no input at all, lands at 13,615.