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, 15 hours to paint, and 7 hours to fire. if the workshop has 116 hours for prep time, 64 hours for painting, and 110 hours for firing, 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

A. 8 wreaths, 6 trees, 2 sleighs Nothing much to do for this problem except to try each option and see if it meets the constraints of available time. So let's check them out.
   
A. 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. All three values are less than or equal to the constraints of 116, 64, and 110. This option will work.
   
B. 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, can't do this option. Don't bother to calculate how many hours of firing needed.
       
C. 9 wreaths, 7 trees, 3 sleighs prep = 9 * 3 + 7 * 14 + 3 * 4 = 137 hours. 137 is more than the allowed 116, can't do this option. Don't bother to calculate how many hours of painting or firing needed.
       
D. 2 wreaths, 8 trees, 6 sleighs prep = 2 * 3 + 8 * 14 + 6 * 4 = 142 hours. 142 is more than the allowed 116, can't do this option. Don't bother to calculate how many hours of painting or firing needed. Of the 4 choices available, only option "A" falls under the required time constraints.