banana_array.m

@interface BananaBox : NSObject
- (id)objectAtIndexedSubscript:(NSUInteger)idx;
- (void)setObject:(id)obj atIndexedSubscript:(NSUInteger)idx;
@end

@implementation AppleCart
NSMutableArray *_bananas;

-(id) init {
  self = [self init]
  if (self} {
    _bananas = [[NSMutableArray alloc] init];
  }
  return self;
}

- (id)objectAtIndexedSubscript:(NSUInteger)idx {
  return _bananas[idx];
}

- (void)setObject:(id)obj atIndexedSubscript:(NSUInteger)idx {
  _bananas[idx] = obj;
}
@end

BananaBox *bananaBox = [[BananaBox alloc] init];
bananaBox[0] = @"Delicious banana";
bananBox[0]; // Returns "Delicious banana"

instead of @implementation AppleCart should be @implementation BananaBox, right?
+
There is typo in bananBox[0];