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The Gardner Theater, a community playhouse, needs to determine the lowest-cost production budget for an upcoming...

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The Gardner Theater, a community playhouse, needs to determinethe lowest-cost production budget for an upcoming show.Specifically, they have to determine which set pieces to constructand which, if any, set pieces to rent from another local theater ata predetermined fee. However, the organization has only two weeksto fully construct the set before the play goes into technicalrehearsals. The theater has two part-time carpenters who work up to12 hours a week, each at $10 an hour. Additionally, the theater hasa part-time scenic artist who can work 15 hours per week to paintthe set and props as needed at a rate of $15 per hour. The setdesign requires 20 flats (walls), two hanging drops with paintedscenery, and three large wooden tables (props). The number of hoursrequired for each piece for carpentry and painting is shownbelow:

CarpentryPainting
Flats0.5  2.0
Hanging drops212
Props3

  4.0

Flats, hanging drops, and props can also be rented at acost of $75, $500, and $350 each, respectively. How many of eachunit should be built by the theater and how many should be rentedto minimize total costs?

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