Question

A ceramics 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?

Answer 1

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

Answer 2

Out of the 4 choices available, only option "A" falls under the required time constraints.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

 

1.

8 wreaths, 6 trees, 2 sleighs

prep = 8 * 3 + 6 * 14 + 2 * 4 = 116 hours.

paint = 8 * 2 + 6 * 3 + 2 * 15 = 64 hours.

fire = 8 * 9 + 6 * 4 + 2 * 7 = 110 hours.

Here, All three values are less than or equal to the constraints of 116, 64, and 110.

 

2.

6 wreaths, 2 trees, 8 sleighs

prep = 6 * 3 + 2 * 14 + 8 * 4 = 78 hours.

paint = 6 * 2 + 2 * 3 + 8 * 15 = 138 hours.

138 is more than the allowed 64.

     

3.

9 wreaths, 7 trees, 3 sleighs

prep = 9 * 3 + 7 * 14 + 3 * 4 = 137 hours.

Here, 137 is more than the allowed 116.

     

4.

2 wreaths, 8 trees, 6 sleighs

prep = 2 * 3 + 8 * 14 + 6 * 4 = 142 hours.

142 is more than the allowed 116,

Thus, out of the 4 choices available, only option "A" falls under the required time constraints.

Learn more about this concept;

https://brainly.com/question/5084407

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The remaining part of the question;

"How many of each can be made?

A. 8 wreaths, 6 trees, 2 sleighs

B. 6 wreaths, 2 trees, 8 sleighs

C. 9 wreaths, 7 trees, 3 sleighs

D. 2 wreaths, 8 trees, 6 sleighs"