Step 1 :First, calculate the total number of mugs and bowls made by the four people at Pia's Pottery Shop. Each person made 29 mugs and 18 bowls, so the total number of objects made by each person is \(29 + 18\). Multiply this by 4 to get the total number of objects made by the four people, which is \(4 * (29 + 18) = 188\).
Step 2 :Next, calculate the total number of mugs and bowls made by the three people at Jason's Craft Shop. Each person made the same number of mugs as a person at Pia's Pottery Shop, which is 29, and twice as many bowls, which is \(2 * 18 = 36\). So the total number of objects made by each person at Jason's Craft Shop is \(29 + 36\). Multiply this by 3 to get the total number of objects made by the three people, which is \(3 * (29 + 36) = 195\).
Step 3 :Finally, add the total number of objects made by the people at Pia's Pottery Shop and Jason's Craft Shop to get the total number of objects made by the seven people. This is \(188 + 195 = 383\).
Step 4 :The seven people made a total of \(\boxed{383}\) objects.