Doris Day will be 89 in two weeks, which makes her exactly half a century too old to play the lead in “Admission.” That’s a pity, as perhaps only she could have done it justice – if it had been made in 1958.

In the event, we get Tina Fey as Portia Nathan, a role that does justice neither to her intelligence nor comic skills. Portia gave a baby away for adoption 18 years ago; now, as an admissions officer at Princeton, she believes that candidate Jeremiah Balakian (Nat Woolf) may be her son.

She’s egged on by John Pressman (Paul Rudd), who runs the alternative school where the genius Jeremiah excelled after nearly failing at a public high school. Naturally, Portia falls in love with John, who represents the free thinking she no longer encounters in her own rigid office.

The script by Karen Croner, who adapted Jean Hanff Korelitz’s novel, bears no examination. The usual clichés are in place, from a middle schooler who speaks truth to adults to the philandering boyfriend who bluntly dumps Portia. (Why hire Michael Sheen for so shallow a role?)

The screenplay has an antifeminist streak that amounts almost to misogyny: A woman can’t be happy unless she has a child, a useful career can’t satisfy her, and women who do live alone become harpies. Portia’s mother (Lily Tomlin), who has a tattoo of Bella Abzug on her arm, is a rude, selfish dolt – until she spends a happy night in the sack with a man.

Why Fey consented to this material baffles me, unless she’s being offered nothing better. She can’t play a woman stupid enough to live with a guy for a decade and have no idea he’s cheating on her, though her energy and emotions infuse the role with a shade of dignity. She and Woolf have a quiet rapport, but Rudd merely gives the Paul Rudd performance he hasn’t varied since 1995.

Nor do I understand why Princeton lent its name and locations to this project. On the evidence of “Admission,” its alumni interviewers are clods, its admissions officers can’t distinguish between creativity and conformity – indeed, they prefer machine-tooled candidates likely to achieve measureable, preferably financial, success – and even campus tour guides insult the students they show around. I suppose universities need to pay the bills, too.