Solve the problem.
-A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 10 hours to fire. A platter takes 17 hours to
Prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 15 hours to paint,
And 7 hours to fire. If the workshop has 134 hours for prep time, 64 hours for painting, and 118 hours for
Firing, how many of each can be made?
A)8 serving bowls, 6 platters, 2 bread baskets
B)6 serving bowls, 2 platters, 8 bread baskets
C)2 serving bowls, 8 platters, 6 bread baskets
D)9 serving bowls, 7 platters, 3 bread baskets

Question

Quizplus · Accepted Answer

To solve this problem, we can use a system of equations.
Let:
- x be the number of serving bowls
- y be the number of platters
- z be the number of bread baskets

Then we can write the equations:
3x + 17y + 4z <= 134 (since there are only 134 hours for prep time)
2x + 3y + 15z <= 64 (since there are only 64 hours for painting)
10x + 4y + 7z <= 118 (since there are only 118 hours for firing)

We want to find integers x, y, and z that satisfy all three equations.

We can solve this system of equations using trial and error or substitution. One possible solution is:

x = 8 (since 3x = 24 hours for prep, which is less than or equal to the limit of 134 hours)
y = 6 (since 17y = 102 hours for prep, which is less than or equal to the limit of 134 hours)
z = 2 (since 4z = 8 hours for prep, which is less than or equal to the limit of 134 hours)

Checking the other constraints, we see that this solution satisfies all three:

2x + 3y + 15z = 64 hours for painting
10x + 4y + 7z = 118 hours for firing

Therefore, the best choice is (A) 8 serving bowls, 6 platters, 2 bread baskets.

Solve the Problem. -A Ceramics Workshop Makes Serving Bowls, Platters, and Bread Baskets