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They say the staff event - also known as "Whānau Friday" - could cost up to $500,000 over the life of the project.
But Waka Kotahi NZ Transport Agency said it would cost about $50,000 and was good for morale.
The $280 million Te Ara o Te Ata: Mt Messenger Bypass is a new 6km route on State Highway 3 about 50km north of New Plymouth. Waka Kotahi says it will improve safety, be more resilient and save time.
But opponents are angry about the 30 hectares of bush being sacrificed for the project, saying the existing road should have been upgraded instead.
"The $500,000 figure was the figure told to us and one of the people working on the project, you know, it was part of one of their meetings and discussions and they said the budget was $500,000 over six years."
At first Gibbs thought that figure was ridiculous, but then he broke out the calculator.
"So divide $500,000 by six years and it's $83,000 a year. So, then I divided it by 52 and I forget the sum, but say we got $8 pies and it's 200 pies a week, you know the calculation that we were told, the price that we were told probably seems reasonable if you were buying 200 pies a week at $8 over six years."
Gibbs said the money would be better spent on repairing the region's pothole-ridden highways.
Pie criticism 'petty'
But New Plymouth Mayor Neil Holdom - a vocal critic of Waka Kotahi's road maintenance programme - had no appetite for that argument.
"If you think, what does a good employer working in a reasonable remote site do and anybody who begrudges someone working hard, an $8 pie once a month sounds pretty petty to me.
"Now this is a big strategic project really important for connecting Taranaki to the north, and I think given the amount of work those people out there are being asked to do, shouting them a pie once a month sounds like a good investment in people."
Holdom said it was a bit rich for opponents of the project, who had cost the country millions of dollars fighting it through the courts, to complain about the cost of the pies.
In a statement, Te Ara o Te Ata project spokesperson Caleb Perry said Whānau Friday was an opportunity for staff to come together, enjoy kai and celebrate project milestones.
"A range of locally bought food, in addition to home baking on occasion, is available for Whānau Friday. The cost of the once-a-month event is approximately $400. Some of the food is bought at New World in Waitara, and other food is bought through a New Plymouth-based supplier. Roughly 80 to 100 people participate."
Perry said Whānau Friday ran as a weekly event for a year, but was now run monthly and was highly valued by staff.
"People on the project are working in a remote environment in what can be challenging conditions. Many workers are also in positions and locations which mean they only connect with a few people each day.
"The workers agree that Whānau Friday played an incredibly important role in connecting team members, and looking after people's morale and well-being."
Waka Kotahi estimated Whānau Friday would cost about $50,000 over the life of the project.
Most customers at Andre's Pies & Patisserie in New Plymouth did not begrudge workers a free pie.
Paul gave it a conditional okay.
"I think it's a reasonable perk considering they can't just wander down the local pie shop like I can. I think the key thing is hopefully it's going to improve productivity and we get the job done on time within budget and the pie situation doesn't tip them into the red."
One woman who preferred not to be name did not agree with it.
"No, they don't need to have those pies."
But Lynne was all right with it.
"I think that's fair enough cos that's a hard job out there."
A motor mechanic was not sure.
"I don't know spending that much money on pies for lunch seems maybe over the top, but then they're in an isolated area."
Russell was all good with it.
"Being out there in the middle of nowhere, I think the least they can do is give them a pie on a Friday."
And André's Pies owner André Glen - who said it was not him supplying them - reckoned it was a great move.
"They work pretty hard and you know, they love pies - that's what workers do, yeah."
He had some recommendations if Waka Kotahi wanted to come calling.
"I can't say for everyone, but I reckon mince and cheese is one of our most popular although the chunky steak now is getting real popular. It's a real man's meal, yeah."
Waka Kotahi is in an ongoing court battle to acquire land it still needs for the bypass via the Public Works Act. When that was secured, it estimated it would take a further four years to complete the project.