Question

5. 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), two hanging drops with painted scenery, and three 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 unit should be built by the theater and how many should be rented to minimize total costs?

Gardner Theater
Hours Required/Piece	Carpentry	Painting
Flats	0.5	2.0
Hanging Drops	2.0	12.0
Props	3.0	4.0
Hours Available	48.0	30.0
Labor Rate/hour	$10.00	$15.00

Answer 1

Below image gives the cost of production which would be required keeping in mid the time available of carpenter and artist. The optimum cost of production would be the lowest cost at the bottom of the calculation (Total Cost of Production) for which we have Carpenters and Artist time indicator as "Yes".

So for production cost to be minimum

we would need to :

Item	Inhouse	Rented
Flats	0	20
Drops	1	1
Props	3	0