The Gardner Theater, a community playhouse, needs to determine the lowest-cost production budget for an upcoming show. Specifically, they have to determine which set pieces to construct and which, if any, set pieces to rent from another local theater at a predetermined fee. However, the organization has only two weeks to fully construct the set before the play goes into technical rehearsals. The theater has two part-time carpenters who work up to 12 hours a week each at $10 an hour. Additionally, the theater has a part-time scenic artist who can work 15 hours per week to paint the set and props as needed at a rate of $15 per hour.

The set design requires 20 flats (walls), 2 hanging drops with painted scenery, and 3 large wooden tables

(props). The number of hours required for each piece for carpentry and painting is shown below:

Carpentry Painting Flats 0.5 2.0 Hanging Drops 2.0 12.0 Props 3.0 4.0 Flats, hanging drops, and props can also be rented at a cost of $75, $500, and $350 each, respectively.

How many of each units should be built by the theater and how many should be rented to minimize total costs?