Question

Q5a) A leading company in Delhi is planning to rent houses and open spaces.
The houses are in three categories namely, having three bedrooms, two bed-
rooms and single bedroom homes. A market survey conducted by a team indi-
cates that a maximum of 650 three bedroom homes, 500 two bedroom homes
and 300 single bedroom homes can be rented. Also, the number of three bed-
room homes should be at least 60% of the number of two bedroom and single
bedroom homes. Open space is proportionate to the number of home units
at the rates of at least 10 sq.ft, 15 sq.ft and 18 sq.ft for three bedroom, two
bedroom and single bedroom homes respectively. However, land availability
limits open space to no more than 10000 sq.ft. The monthly rental income is
estimated at Rs. 45000, Rs. 56250 and Rs. 90000 for single bedroom, two
bedroom and three bedroom homes respectively. The open space rents for Rs.
7500/sq.ft. Formulate the above as an LPP so as to get maximal revenue.
b) Convert the following problem to standard form explaining the various
steps.
Minimize: Z = −3x1 + x2 + x3
Subject to: x1 − 2x2 + x3 ≤ 11
− 4x1 + x2 + 2x3 ≥ 3
2x1 − x3 = −1
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0

Answer 1