Aceramics workshop makes wreaths, trees, and sleighs for sale at christmas. a wreath takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. a tree takes 14 hours to prepare, 3 hours to paint, and 4 hours to fire. a sleigh takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. if the workshop has 127 hours for prep time, 104 hours for painting, and 133 hours for firing, how many of each can be made?

If all things can be made at the same time, then it would look something like this(all numbers should be rounded down):

127 of Prep: Wreath:127/3 = 42 prepped
127 of Prep: Tree:127/14 = 9 prepped
127 of Prep: Sleigh:127/4 = 31 prepped

104 of Painting: Wreath:104/2 = 52 painted(but because only 42 were prepped, your number will be 42 still)
104 of Painting: Tree:104/3 = 34 painted(As stated above, but with only 9)
104 of Painting: Sleigh:104/17 = 6 painted(this number will overwrite the number of prepped sleighs as only 9 could be painted in the allotted time.)

133 of Firing: Wreath:133/9 = 14 ready to go
133 of Firing: Tree:133/4 = 33(but only nine were painted so the number ready to go is 9) 
133 of Firing: Sleigh:133/7 = 19(but only 6 are ready to go)

Final Results: Wreath - 14
                       Tree - 9
                      Sleigh - 6

Wreaths- 42 prep,  52 painted, 14 fired
Trees- 9 prep, 34 painted, 33 fired
Sleighs- 31 prep, 6 painted, 19 fired

How many can be made:
Wreaths= 14
Trees= 9
Sleighs= 6

128/3reason being 5 and 1/3 = 16/316/3 • 2/3 = 32/31 and 1/3 = 4/3 32/3 • 4/3 this will equal 128/3