Solve the problem.
-A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 8 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, 13 hours to paint, and 7 hours to fire. If the workshop has
117 hours for prep time, 71 hours for painting, and 101 hours for firing, How many of each can be made?
A)7 wreaths, 6 trees, 3 sleighs
B)6 wreaths, 3 trees, 7 sleighs
C)3 wreaths, 7 trees, 6 sleighs
D)8 wreaths, 7 trees, 4 sleighs

Question

Quizplus · Accepted Answer

To solve this problem, we need to set up a system of equations based on the hours required for each item:
3W + 14T + 4S ≤ 117 (hours available for preparation)
2W + 3T + 13S ≤ 71 (hours available for painting)
8W + 4T + 7S ≤ 101 (hours available for firing)

where W, T, and S represent the number of wreaths, trees, and sleighs respectively. We want to find an integer solution (since a fraction of a wreath, tree, or sleigh doesn't make sense), and check which option(s) satisfy all three constraints.

Option A) 7 wreaths, 6 trees, 3 sleighs:
3(7) + 14(6) + 4(3) = 105, which is less than or equal to 117. 
2(7) + 3(6) + 13(3) = 68, which is less than or equal to 71. 
8(7) + 4(6) + 7(3) = 101, which is equal to 101.

Therefore, option A) is a valid solution, and the best one since it uses up most of the available time for preparation and painting while meeting the firing constraint exactly.

Solve the Problem. -A Ceramics Workshop Makes Wreaths, Trees, and Sleighs for Sale