When Maggie eats a magazine, Marge demands that Homer go to the grocery store to pick up some food. While there, Homer (and all the other shoppers) insult, abuse and make unreasonable demands of the bag boy (Homer constantly demanding that the bags be arranged in different orders, Agnes Skinner demands all her items put into one bag without the bag being heavy), causing all the bag boys in Springfield to go on strike. The bag boys also prevent anyone from carrying their groceries to their cars. When all the food in the house is gone, Homer becomes desperate and goes in the search of some food. Santa's Little Helper finds a 30 year old box of Animal crackers which Homer steals away and despite protests about the cookies expiry Homer digs in without hesitation. He bites into a giraffe-shaped cracker and realizes it's made of gold, which means that the family has won a trip to Africa. The makers of the animal crackers (who point out that not only did the contest end decades ago, they no longer make animal crackers and that the box is not a binding contract) refuse them the trip, but when Homer hurts himself on the corner of the box, they reconsider, as they don't want to be sued.
When they arrive in Ngorongroro, Tanzania, the Simpsons see billboards with messages such as "Hail President Muntu", who their guide, Kitenge, informs them recently seized power. We then see the family staying in a treetop hotel, then going on safari in the Masai Mara, visiting Olduvai Gorge, and spending a day with some Maasai tribesmen. The family then join the tribesmen in a tribal dance, and Homer, while attempting to play the drums, accidentally beats the rear end of a hippopotamus, which enrages it. They use a tribal shield as a makeshift raft to escape down the river, but take a wrong turn, get swept over a waterfall, and end up far from the Maasai village. Suddenly, a chimpanzee appears, and lead them to "Joan Bushwell's Chimp Refuge", which is run by Dr. Joan Bushwell (who is voiced by Tress MacNeille). Dr. Bushwell tells the Simpsons that she is in Africa because she is researching chimpanzees, but, when Greenpeace arrive at the refuge, the family discover that she has enslaved the apes and is making them work in a diamond mine beneath the refuge. Fearing the repercussions for what she has done, Dr. Busswell attempts to bribe the Simpsons and the people from Greenpeace with handfuls of diamonds. The next scene starts with the family sitting on the plane to go back to Springfield, with all of them but Lisa carrying a small fortune in diamonds. Out of the window of the plane, they see a new billboard which reads "Hail President Kitenge", with a picture of their old guide in the presidential robes that Muntu was wearing earlier in the episode. Marge asks, "What happened to President Muntu?" Muntu then appears dressed as a flight attendant and says, "I don't want to talk about it." Muntu begins handing out peanuts, and the family all laugh as the plane takes off.