A small plant in Pembroke Park churns out more than 40,000 Jamaican-style patties a day and can hardly keep up with demand.

Hotpie produces five types of Jamaican patties — mild beef, spicy beef (the biggest seller), island curry chicken, jammin’ jerk chicken and vegetable — packages them and ships the frozen patties to supermarkets, schools, gas stations, convenience stores, restaurants and other wholesale buyers in Florida and an expanding number of other states. Buyers can also order smaller quantities and pick up their patties at the Hotpie plant. Hotpies sell wholesale for $20-21 for a box of 24.

Over the past 26 years, Dennis Chung, the founder and president of Hotpie, has carved out a successful niche in the highly competitive processed-foods sector.

Chung, originally from Jamaica, moved to Canada in the 1960s. While he was studying to obtain his degree in mechanical engineering at the University of Toronto, Chung learned how to make Jamaican patties, opened up a small bakery called Mr. Spicee, and started selling patties.

“I didn’t know a thing about Jamaican patties except that I liked eating them,” Chung said.

After graduating and working for several years as an engineer in Canada, Chung and his wife, Olivia, vice president of Hotpie, moved to South Florida in the 1980s. They began making patties at home, trying out different recipes with friends and family “until we got it right,” he said.

In 1986, the Chungs set up Hotpie, bought some used patty-making equipment and rented a bay in an industrial area.

“We started out on a shoestring,” Dennis Chung said.

Building on the taste for patties among South Florida’s Jamaican community, and introducing their products to businesses where Latinos typically buy empanadas, Hotpie began growing as customers tried the patties and came back for more.

Today, the company has 25 employees (35 in the winter high season) and six bays at the original site (10,000 square feet). It has maxed out production at more than 40,000 patties a day in two shifts at its USDA-inspected plant and is planning to expand. Sales rose over 30 percent last year and are going strong in 2012, Dennis Chung said.

In addition to Dennis and Olivia, their sons, Paul and Mark, share management responsibilities.

The company sells under its own Hotpie brand, as well as Island Joe’s (for food stores) and Jamaica Makins, and is expanding sales to reach more customers in the United States and the Caribbean. Hotpies are already being sold in the Bahamas, Grenada and the Turks & Caicos.