Question

1. A shop makes tables and chairs. Each table takes 9

hours to assemble and 3 hours to finish. Each chair takes
4 hours to assemble and 2 hour to finish. The assemblers
can work for at most 250 hours each week, and the
finishers can work for at most 80 hours each week.
Write the inequalities representing the number of hours.
Let t be the number of tables and c be the number of 2
chairs.

Answer 1

9t + 4c ≤ 250

3t + 2c ≤ 80

Explanation:

t is the number of tables

c is the number of chairs

Each table takes 9 hours to assemble and 3 hours to finish, so t tables take 9t hours to assemble and 3t hours to finish.

Each chair takes 4 hours to assemble and 2 hours to finish, so c chairs take 4c hours to assemble and 2c hours to finish.

Therefore, total assembly time is 9t + 4c. Total finishing time is 3t + 2c.

Total assembly time is at most 250, and total finishing time is at most 80.

9t + 4c ≤ 250

3t + 2c ≤ 80