Q: The company must determine how many storage rooms of each size to build,. The problem...

Q:

The company must determine how many storage rooms of each size to build,. The problem formulated as linear progrram (LP), as follows: maximize Z=40 X1 + 30 X2, subject to 2 X1 + 4 X2 <=200, 100 X1 + 50 X2 <= 4000, X1 <= 35, X1 & X2 => 0 Q1) graph all the constraints and identify the feasible region fro this LP. Q2) what is the optimal soulution for this problem, what the optimal x1 and x2 values and the corresponding earning level? Q3) briefly explain how you would determinte the dual price of the adverising budget constraint. Q4) if the rental limit constraint is decrease from 35 to 23, by how much will the monthly earnings change? Q5) several assumptino must implicitly be made to formulate and solve this problem using a linear program. Identify at least one LP assumption which is violated in this context which may not be appropriate when the decision variables relate to the number of storage units develop.

Expert Solution

The LPP would be formulated as

MAX z = 40x1 + 30x2
subject to
2x1 + 4x2 <= 200
100x1 + 50x2 <= 4000
x1 <= 35
and x1,x2 >= 0

Q1.

The feasible region is shown in the graph in the image attached as IMAGE1

Q2.

The maximum value of the above objective function is z=2000 and occurs at the extreme point (20,40), which is the optimal solution.

Q4.

Changing the rental limit constraint from 35 to 23 does not change anything with respect to the optimal solution. This can be understood after viewing the graphical part of the solution which is uploaded as IMAGE2. The solution is thus z=2000 and occurs at the extreme point (20,40).

Q5. The data related to the above problem is crisp and clear and no assumptions need to be made regarding the formulation of LPP.

keosha answered 1 year ago

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