Question

A banquet hall offers two types of tables for rent: 6-person rectangular tables at a cost of $20 each and 10-person round tables at a cost of $41 each Kelly would like to rent the full for a wedding banquet and needs tables for 230 people. The room can have a maximum of 39 tables and the hall only has 10 rectangular tables available. How many of each type of table should be rented to minimize cost and what is the minimum cost?

The minimum cost is achieved with 6-person rectangular tables and 10-person round tables

Answer 1

To minimize cost and seat 230 people, Kelly should rent 10 rectangular tables and 17 round tables, resulting in a minimum cost of $897.

Step-by-step explanation:

The student's question pertains to finding the minimum cost of renting tables for a wedding banquet while accommodating 230 people with constraints on the number of tables and types available. The rectangular tables can seat 6 people and cost $20 each, while the round tables can seat 10 people and cost $41 each. The hall has a maximum of 39 tables and only 10 rectangular tables available.

To minimize the cost, we must first address the constraint of seating 230 people. Using only the 10 available rectangular tables, we can seat 10 x 6 = 60 people. Therefore, we need to seat an additional 230 - 60 = 170 people. We will use round tables for this, which seat 10 people each. To find the number of round tables needed, we divide 170 by 10, which gives us 17 round tables.

Now we must ensure that the total number of tables does not exceed the maximum of 39. With 10 rectangular tables and 17 round tables, we have 10 + 17 = 27 tables in total, which is within the limit.

The cost of renting the rectangular tables is 10 x $20 = $200. The cost of renting the round tables is 17 x $41 = $697. Therefore, the minimum cost for renting the tables is $200 + $697 = $897.