Question

 

Thapar theatre company needs to determine the lowest cost production budget for an upcoming theatre show. Specifically, they will have to determine the lowest which set pieces to construct and which pieces must be rented from another company at a pre-determined fee. The time available for constructing the set is two weeks after which rehearsals commence. To construct the set, the theatre has two part-time carpenters who work upto 12 hours a week and each at Rs 100 per hour. Additionally, the scene artist can work 15 hours per week at Rs 150 per hour

The set design requires 20 walls, 2 hanging drops with pained scenery and 3 large wooden tables serving as props. The number of hours required for each piece for carpentry and painting is given below.

	Carpentry	Painting
Flats	0.5	2.0
Hanging Drops	2.0	3.0
Wooden Tables(props)	3.0	4.0

Flats, hanging drops and props can also be rented at a cost of Rs 750, Rs 5000 and Rs 3500 each.

How many of each unit should be built by the theatre company and how many units should be rented to minimize costs?

Answer 1

Excel solution file link: https://1drv.ms/x/s!AkW5WQDSTr7Dhm2tLX3OYX0sNJTL

x1	x2	x3	y1	y2	y2	Min	Obj
350	750	900	750	5000	3500		16800
6	2	3	14	0	0
S.t						LHS		RHS
0.5	2	3				16	<=	48
2	3	4				30	<=	30
1			1			20	<=	20
	1			1		2	<=	2
		1			1	3	<=	3

Therefore

Constructed Units:

Flats: 6 units

Hanging Drops: 2 units

props: 3 units

Rented Units:

Flats: 14 units

Hanging Drops: 0 units

props: 0 units

Min cost = Rs. 16800