Personal Mini Warehouses is planning to expand its successful Nashua business into Lowell. In doing so, the company must determine how many storage rooms of each size to build. The problem has been formulated as a linear program (LP),as follows:

 

maximize Z=80x1	+	50x2			(Monthly earnings)
subject to: 4x1	+	4x2		480	(Advertising budget)
80x1	+	40x2		5600	(Square footage required)
x1				50	(Rental limit expected)
x1	&	x2		0

where x1 is the number of large spaces developed, and x2 is the number of small spaces developed.

 

1.Graphall of the constraints in the space below and identify the feasible region for this LP.

 

2.What is the optimal solution for this problem, i.e., what are the optimal x1 and x2 values and the corresponding earnings level?

3.Briefly explain how you would determine the dual price of the advertising budget constraint. (Alternatively, calculate the dual price and show the steps taken.)

 

4.If there nit aliment constraint is decreased from 50 to 40, by how much will the monthly earnings change?

 

 

5.Several assumptions must implicitly be made to formulate and solve this problem using a linear program. Identify at leas tone Assumption which is violated in this context, i.e., which may not be appropriate when the decision variables relate to the number of storage units developed.