Q5a) A leading company in Delhi is planning to renthouses 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 teamindi-
cates that a maximum of 650 three bedroom homes, 500 two bedroomhomes
and 300 single bedroom homes can be rented. Also, the number ofthree bed-
room homes should be at least 60% of the number of two bedroom andsingle
bedroom homes. Open space is proportionate to the number of homeunits
at the rates of at least 10 sq.ft, 15 sq.ft and 18 sq.ft for threebedroom, two
bedroom and single bedroom homes respectively. However, landavailability
limits open space to no more than 10000 sq.ft. The monthly rentalincome is
estimated at Rs. 45000, Rs. 56250 and Rs. 90000 for single bedroom,two
bedroom and three bedroom homes respectively. The open space rentsfor Rs.
7500/sq.ft. Formulate the above as an LPPso as to get maximal revenue.
b) Convert the following problem to standard form explaining thevarious
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
