Suppose somebody gave you a stock tip and told you that nearly 30 percent of the company's earnings come from the Mideast. You probably would think the tipster had flipped. Considering all the turmoil and uncertainty in the Mideast, such a company would likely be the worst kind of investment at this point, you'd speedily conclude.

Well, for now at least, you'd be dead wrong. The share of one such company, Los Angeles-based Whittaker Corp., one of the conglomerate darlings -- and disasters -- of the late 1960s, have scooted to a new 1979 high. After having traded as low as 4 1/4 in 1977 and 7 1/8 in 1978, the stock of the $1 billion company recently surged past 18 in accelerated trading activity.

Whittaker's Mideast activities -- which are expanding -- cheifly involve administering a health-care program for the Saudi Arabian government, primarily the management and operation of three hospitals. And this April, the company announced receipt of a $110 million contract to manage and operate a hospital in Abu Dhabi.

When you think about it, Whittaker has engineered a remarkable comeback. It started out as an aerospace company in 1947, but then went on an to acquiremore than 100 different firms between 1967 and 1970. Reflecting its meteoric growth, Whittaker's shares went through the roof, rising from 6 3/8 in 1967 to 45 7/8 just a year later. But then the roof cave in (as did its stock) when the company virtually lost control over the management of its various businesses in 1970. It was also the year in which the debt-ridden and highly leveraged company was stung with an $8.5 million loss on some $800 million in sales. Whittaker seemed headed for the scrap heap. But then came a major restructuring of the company under a new chief executive (Joe Alibrandi, formerly a senior vice president of Raytheon), the subsequent divestiture of 92 businesses and deeper involvement in the fast-growing hospital management of life sciences field.

As things stand now, the company's earnings are booming.

In fiscal 1978 (ended Oct. 31), Whittaker earned $2.12 a share on sales of $884 million. In the next couple of weeks the company will report its fiscal 1979 results, and they're going to look very good. In a recent chat, Alibrandi told me earnings will be about $3 a share on sales of about $1.07 billion. "We're strong right across the board; every group (including the marine, metals, railroad-car-manufacturing and chemicals sectors) showed an increase in fiscal'79," he said.

Some chief executives I've met come across as touts; Alibrandi's not one of them, in my mind. He thought carefully and did some pencil-pushing before responding to questions on Whittaker's prospects. His expectations are pretty darn impressive. He expects fiscal 1980 earnings (including the proposed acquisition of General Medical Corp.) to climb about 33 percent to about $4 a share on sales of $1.3 billion. At that point, the medical business should represent 40 percent of earnings, he said.

Looking to fiscal 1981, Alibrandi sees another big jump -- and earnings gain to about $6 a share on a $1.6 billion volume. This assumption includes major expansion of the hospital facilities, considerable earnings improvement from the General Medical acquisition, additional medical acquisitions and an overall average annual earnings growth of 15 percent from the various nonmedical businesses.

This prediction excludes the benefits to per-share earnings of a reduction of outstanding shares through a stock repurchasing program. The company plans to buy back 1 million shares of its roughly 14 million shares outstanding (fully diluted); so far, it has bought in about 100,000 shares. The full purchase would boost per-share net another 5 to 7 percent.

Alibrandi had some additional good news for Whittaker's holders. He told me that either in January or February the Whittaker board -- "unless the world goes to hell in a handbag" -- will consider doubling the annual 50-cent dividend to $1.

It all sounds terrific -- except for that scary Mideast exposure. What happens, I asked Alibrandi, if you're booted out of the Mideast?

"I don't discount it, and we're hedged to the maximum extent -- all Mideast payments to Whittaker are made in advance -- but I think it's highly unlikely," he replied. "I can't believe we'd sit around and let 9.4 million barrels a day (the Saudi daily production) be jeopardized by a takeover of the country by a new regime . . . " A Saudi national has a minor interest in Whittaker's Saudi operations.

Considering the company's seemingly cheap stock price -- based on its above-average earnings prospects -- the Mideast concern obviously is substantial. And well it should be. But some brokerage firms are willing to look beyond that. One is the small, well-regarded research house of Furman Selz Mager Dietz & Birney. Furman Selz, which has been running a hot hand in a number of its recent stock recommendations, has just added Whittaker to its buy list. It also notes the obvious Mideast risks, but still rates Whittaker as "an undervalued company with an exciting life-sciences thrust."

Alibrandi has a similar view of the life-sciences business. He told me it should be running at a $600 million annual sales rate after the General Medical acquisition in March. And some time in the 1983-1984 period, "hopefully it'll be at a $1 billion," he said.