C3 Inc., a 12-year-old Reston computer systems firm, yesterday announced an offer to sell the first public shares of the company for $33.6 million. Half the stock will be sold by the company and the remainder by current company stockholders.

The company, which had sales of $13.9 million and profits of $2.3 million for the fiscal year ended March 30, does almost 90 percent of its business with defense-related agencies. Only about 4 percent of the company's sales are to commercial customers. The individual sales range from $100,000 to $1 million.

C3 designs, assembles and markets computer systems and offers training, support services and maintenance for the equipment. The company's profits have risen from about $750,000 in its fiscal 1977 to $2.3 million this year.

The company said in a filing statement with the Securites and Exchange Commission that it plans to use the money from the stock sale to "finance delivery orders" and to provide capital for the company's growth. Over the next 15 months, C3 said the company will finance about $7 million of equipment leases.

Purchasers of the 1.1 million shares of C3 stock will pay between $24 and $28 a share for stock now worth $2.67 a share. Including the money the company will get for the new offering, C3 will have a book value of $5.93 a share.

The offering is being underwritten by Donaldson, Lufkin & Jenrette and E.F. Hutton & Co. Inc.

Of the 1.1 million shares, 600,000 are being sold by the company and 500,000 are being sold by current stockholders. When the sale is completed, current stockholders will continue to own about 3 million shares, approximately 73 percent of the outstanding common stock, for which they paid an average of 84 cents a share.

The two principal shareholders are the founder of the company John G. Ballenger, 49, now chairman, president and treasurer; and John D. Vazzana, 36, vice president for finance. Last year, Ballenger earned $305,523 in salary and fees and Vazzana earned $200,127.

Ballenger now owns almost 29 percent of C3 -- more than 1 million shares -- and after selling 125,000 shares will control 21.5 percent of the company, according to the filing with the SEC.