Why would legislators most likely ask interest groups to shape public policy?

because interest groups volunteer to advise lawmakers about issues
because interest groups are paid to advise lawmakers on specific issues
because interest groups donate to their campaigns at election time
because interest groups demand that they be heard on certain issues

The correct answer is C.

Interests groups send representatives to put pressure on members of Congress and other policymakers. They engage in lobbying for particulate issues that they want to push or they help to fund political campaigns at election times.

Interest groups involve themselves in political campaigns to help to elect candidates who favor they positions or to defeat those who oppose them. They donate money to their candidate, so that the candidate has enough money to sponsor his election campaign. The donation is usually done through Political Action Committees ( PACs)  which are associations of interests groups. PAC's contributors write checks for the purpose of campaign donations.

Some critics of interest groups say that they buy influence. Interests groups are closely associated with big businesses and corporations. This gives them a connection to government many ordinary people do not have.

because interest groups demand that they be heard on certain issues

to plan an idea out before