"Cost-effective" means "most economical", "lowest cost", "cheapest".
Joshua . . . charges $25 an hour, says the job will take him 5 hours. If Joshua is hired, then the total cost to get the job done is ($25/hr) x (5 hr) = $125 .
Carmen . . . $20 per hour, 7 hours, total cost ($20/hr) x (7 hr) = $140
Dante . . . $30 per hour, 6 hours, total cost ($30/hr) x (6 hr) = $180
Alicia . . . $20 per hour, 8 hours, total cost ($20/hr) x (8 hr) = $160
Joshua's total bid cost is the lowest, so his company should get the job.
Notice that all of these bids are predictions of something that hasn't happened yet. IF Joshua can actually finish the job in 5 hours, like he says, then he would be the cheapest. But his estimate of the time required is the shortest of all. That's great if he's done this kind of job before. But if he doesn't have experience doing it, I would be a little careful. He could get part of the way through the job and discover that it's going to take him longer than he thought.
There are also certain regional considerations:
-- I live in Chicago, where cost is not always the main factor. Here, you would have to award the job to Dante, because his brother supplies the concrete in the ward where the job will be done, and his niece is dating the alderman of that ward.
-- In California, you'd have to give Alicia the job because the board of directors and management of her company are all women. You should also plan to provide chocolates, flowers, and college scholarships to her administrative staff and IT department relatively soon after the job is completed.