Boeing Co. reported yesterday that a 75 percent increase in sales pushed first-quarter profits to $108.1 million ($1.69 s share) from $45.2 million (71 cents) in the first quarter of 1978. Sales for the period surged to $1.78 billion from $1.02 billion in the Same period a year ago.

T. A. Wilson, chairman of the board of directors, said at the company's annual stockholders meeting that because of the continued heavy jet transport activity, production is to be increased to 28 airplanes a month from 24 by the fourth quarter.

Wilson attributed the increased earnings to the rising sales volume, continue favorable trends on commercial jet transport programs, increased interest income, a substantial reduction in the company's share of losses of Peabody Holding Co. and a lower effective federal income tax rate.

Shareholders, as expected, approved an increase in the company's authorized common shares to 150 million from 75 million.

But Wilson said in response to a shareholder question that the company has no plan at this time to use the additional shares for an acquisition.

Coca-Cola Co. reported a first-quarter profit of $85 million (69 cents a share), up from $75 million (61 cents) a year ago. The company also said its sales increased from $908 million to $1.05 billion.

Separately, Coca-Cola chairman J. Paul Austin told the annual meeting in Wilmington, Del., that the company has signed new contracts with more than half to its U.S. bottlers which permit the company to raise the prices under a formula based on the consumer price index.

A $39.7 million settlement of a tax refund suit raised first-quarter earnings of MCA Inc., to $2.74 a share.

The tax refunds were on the profits of theatrical and television motion picture films for the years 1926 through 1970.

Net income was $63.88 million on operating revenues of $283 million against $21.3 million a year ago on revenues of $236.4 million.