Q1:In the Danson Theater model, how many total hours of carpentry are available?

Q2: In the Danson Theater model, how much does it cost the theater to build a flat?

Q3:Based on your Danson Theater model and your analysis of its results, what is the minimum total cost for the set pieces for the upcoming show?

Q4:Based on your Danson Theater model and your analysis of its results, in the optimal solution, how many props do they build?

The Danson 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: Flats, hanging drops, and props can also be rented at a cost of $75,$500, and $350 each, respectively. How many of each unit should be built by the theater and how many should be rented to minimize total costs? (Hints: How many total hours of carpentry and painting are available? How much does it cost to build each item?)