WASHINGTON — It pays to be the middleman — especially in a time of crisis.

For W.W. Grainger Inc., a big industrial supply company, that meant quickly doubling the price of coveralls in a contract with the U.S. Department of Health and Human Services that is worth as much as $35.8 million. The short of it: Grainger, acting as the silent partner in a deal between the federal government and two other companies, bought coveralls at $4 apiece from DuPont and then sold them to Uncle Sam for $7.96 apiece.

“Yes, these are the same suits,” a spokesperson for the HHS department said. “Grainger is DuPont’s distributor.” The coveralls are used to protect health care workers, first responders and others from the coronavirus.

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For a while, Grainger’s role in the four-way partnership, established through the White House coronavirus task force’s Project Airbridge, was something of a secret.

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Under the deal, the U.S. government paid Federal Express to fly Tyvek, a synthetic material, from a DuPont facility in Richmond, Virginia, to Vietnam, where it was sewn into coveralls at a factory that DuPont uses. DuPont first told NBC News that it sold the suits to the federal government, which paid FedEx to fly the finished product back to the U.S.

But DuPont typically doesn’t sell directly to the federal government and it may have needed a partner for immediate entree into the contracting system. A person familiar with the arrangement said the federal government was specifically interested in purchasing DuPont’s Tyvek-based coveralls.

President Donald Trump, the HHS Department, DuPont and FedEx all heralded the agreement last week. They praised each other, but none of them mentioned Grainger. Later, a DuPont spokesman told NBC News that his company had actually sold the suits to an intermediary but refused to name the company.

Federal contracts revealed that it was Grainger, a Fortune 500 company that has suddenly become a more prominent provider of protective clothing as the government’s response to coronavirus kicked into high gear last month. The HHS department bought the first batch of 2.25 million suits at a total cost of $17.9 million from Grainger and holds an option for a second set of the same size at the same cost.

Though Grainger has a nationwide distribution network, its contract with the HHS department is only for the purchase of the coveralls and the associated paperwork that cleared the way for FedEx to leave Vietnam with the goods and land in the U.S., according to the HHS department spokesperson.

“It’s important to note that the sale price was nearly 10 percent lower than the standard listed price for this off-schedule transaction,” Joseph Micucci, a spokesman for the company, said in an email response to questions from NBC News about what is by far the largest federal contract Grainger has ever won for apparel. "[W]e carefully review all pricing to ensure that any price increases are only the result of our increased costs."

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Grainger lists several styles and sizes of Tyvek coveralls at $221 for packages of 25, a 10 percent cut from which is $7.96 per suit — the amount charged to the HHS Department for the stock DuPont says it sold to Grainger for $4 per unit.

A senior administration official familiar with supply-chain issues said that Vice President Mike Pence's coronavirus task force and its subunits bought as much available stock of personal protective equipment as possible and have worked to use partnerships like Project Airbridge to expedite the process of obtaining material from overseas. In the case of the coveralls, that reduced shipping time from the U.S. to Vietnam and back from 90 days to 10 days.