Question

A starting carpenter can build a rough table in 1 hour, and a rough chair in 45 minutes. A finishing carpenter can finish each table in 48 minutes and finish each chair in 1 hour. Both carpenters work for no more than 8 hours each day. This situation is modeled in the graph below, where x represents the number of tables, and y represents the number of chairs. Is it possible for the two carpenters to complete four tables and five chairs in a day?

Answer 1

It is impossible for the carpenters to complete these chairs and tables in 8 hours.

Answer 2

Let x represent the number of tables, and y represent the number of chairs.

If a starting carpenter can build a rough table in 1 hour, and a rough chair in 45 minutes, then he needs 1·4=4 hours to complete 4 tables and 45·5=225 minutes = 3 hours 45 minutes to complete 5 chairs. In total he needs 7 hours 45 minutes (less than 8 hours).

If a finishing carpenter can finish each table in 48 minutes and finish each chair in 1 hour, then he needs 48·4=192=3 hours 12 minutes to complete 4 tables and 1·5=5 hours to complete 5 chairs. In total he needs 8 hours 12 minutes (more than 8 hours).

Starting carpenter will complete the job and finishing carpenter will not complete the job.

Answer: it is not possible for the two carpenters to complete 4 tables and 5 chairs in a day.