question archive Personal Mini Warehouses is planningto expand its successful Nashua business into Lowell
Subject:ManagementPrice: Bought3
Personal Mini Warehouses is planningto expand its successful Nashua business into Lowell. In doing so, the company mustdetermine how many storage rooms of each size to build. The problemhas been formulated as a linear program (LP), as follows:
maximize Z =80x1 |
+ |
50x2 |
(monthly earnings) |
||
subject to: 4x1 |
+ |
4 x2 |
≤ |
480 |
(advertising budget) |
80x1 |
+ |
40x2 |
≤ |
5600 |
(square footage required) |
x1 |
≤ |
50 |
(rental limit expected) |
||
x1 |
& |
x2 |
≥ |
0 |
where x1 is the number of large spacesdeveloped, and x2 is the number of small spaces developed.
x2 | |||||||||||||||||||||
200 | |||||||||||||||||||||
180 | |||||||||||||||||||||
160 | |||||||||||||||||||||
140 | |||||||||||||||||||||
120 | |||||||||||||||||||||
100 | |||||||||||||||||||||
80 | |||||||||||||||||||||
60 | |||||||||||||||||||||
40 | |||||||||||||||||||||
20 | |||||||||||||||||||||
20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 |
x1
??What isthe optimal solution forthis problem, i.e., what are theoptimal x1 and x2 values andthe corresponding earnings level?
??
Briefly explain how you woulddetermine the dual price of theadvertising budget constraint. (Alternatively, calculate the dual price and showthe steps taken.)
??If therental limit constraint is decreased from50 to 40,by howmuch will themonthly earnings change?
??Several assumptions must implicitly be made to formulate and solve this problemusing a linear program. Identify at least one LP assumption whichis violated in this context, i.e., which may not be appropriate when the decision variables relateto the number of storageunits developed.