Question

Chelsie and her fiancé Vlad have decided to host their wedding reception in the

ballroom at the local golf course. Two types of tables are available to rent 6-person
rectangular tables at a cost of $28 each and 10-person round tables at a cost of $52
each. They need to be able to seat at least 250 people. The ballroom can hold a
maximum of 35 tables. Only 15 rectangular tables are available for the date Chelsie
and Vlad have booked with the club. How many of each type of table should they
rent to minimize cost? Will Chelsie and Vlad be able to stay within the $1,300 budget
they've set for this wedding expense?
a) Yes

b) No

Answer 1

Chelsie and Vlad cannot stay within their $1,300 table rental budget for their wedding reception since renting the necessary number of tables to seat at least 250 people would cost them $1,460, exceeding their budget.

Step-by-step explanation:

To minimize the cost of seating at least 250 people with a combination of 6-person rectangular tables and 10-person round tables, we need to setup and solve a linear optimization problem. Chelsie and Vlad can rent at most 15 rectangular tables, which would seat 90 people (15 tables x 6 people/table), leaving at least 160 people to be seated at round tables. Since round tables seat 10 people each, they would need at least 16 round tables for 160 people. However, they can only have a maximum of 35 tables. So, if they rent all 15 rectangular tables, they can only have 20 round tables (for a total of 35 tables), which would seat an additional 200 people, resulting in seating for a total of 290 people.

The cost for renting 15 rectangular tables would be 15 x $28 = $420, and the cost for renting 20 round tables would be 20 x $52 = $1040. The total cost for tables would then be $420 + $1040 = $1460. Unfortunately, this exceeds their budget of $1300. Therefore, the answer is b) No, Chelsie and Vlad will not be able to stay within the $1,300 budget they've set for this wedding expense.