By Jacob Bunge and Chelsey Dulaney 

DuPont Co. Chief Executive Ellen Kullman defended the company's diverse portfolio of businesses Tuesday, pushing back against an activist investor's public drive to break the company in two.

Ms. Kullman, in her first public comments on the campaign by Trian Fund Management LP, said the chemical company gains unique competitive advantages by developing seeds for farmers, plastics for car makers and a host of other products.

"There is a lot of power in being able to deliver greater capability to [customers] than in being very narrow," Ms. Kullman said in an interview after commenting earlier on Trian's proposal in a post-earnings conference call.

Trian, headed by investor Nelson Peltz, called in September for DuPont to divide into a growth-oriented company focused on agriculture and nutrition and another company focused on industrial materials set up to return cash to shareholders. Trian argued its plan could help eliminate $2 billion to $4 billion in what the firm said were excess annual corporate costs at DuPont, and produce more meaningful scientific discoveries at the resulting companies.

Ms. Kullman, who has led DuPont since January 2009, said "there are points where we and Trian are aligned," such as trimming costs and managing DuPont's broad portfolio of businesses, which range from producing components for high-definition television screens to deicing fluids for airport runways. She said DuPont over the past five years has cut $2 billion in expenses, with plans to cut another $1 billion by 2020, while repurchasing more shares than its peers.

DuPont plans to spin off next year its performance-chemicals business, which makes house paints and materials for nonstick frying pans. The company expects to file documents detailing the plan to U.S. regulators in December, Chief Financial Officer Nick Fanandakis told analysts on the quarterly earnings call.

While Ms. Kullman didn't rule out further changes to DuPont's portfolio--both adding and cutting businesses--she said in the interview that breakup plans must be viewed "in the cold, hard daylight to understand how we create value."

"We take a look at what the breakup costs would be, what the ongoing increased costs would be, what the lost capability would be, and understand that opportunity versus [remaining] together," Ms. Kullman said.

DuPont's current portfolio gives the company advantages in engineering and production capacity, and the flexibility to divert more people and resources to tackle a problem or introduce products more quickly, she said.

Ms. Kullman declined to specify whether DuPont would consider giving Trian, which owns about 3% of DuPont shares, a seat on the Wilmington, Del., company's board. "This is early, from the standpoint of Trian," she said, and investors generally give DuPont "very high marks for strong governance."

DuPont said third-quarter earnings jumped 52% because of lower expenses, despite a 4% decline in agricultural sales due to slowing seed demand.

DuPont reported a profit of $433 million, or 47 cents a share, up from $285 million, or 30 cents a share, a year earlier. Excluding certain items, operating earnings increased to 54 cents a share from 45 cents a share.

Net sales fell 2.9% to $7.51 billion due to the sale of some businesses.

Mr. Fanandakis warned that a sluggish economy in Europe and strengthening U.S. dollar were likely to weigh on DuPont's performance in the coming months.

Write to Jacob Bunge at jacob.bunge@wsj.com and Chelsey Dulaney at Chelsey.Dulaney@wsj.com

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