Personal Mini Warehouses is planning to expand its successful Orlando business i

Question

Personal Mini Warehouses is planning to expand its successful Orlando business into Tampa. In doing so, the company must determine how many storage rooms of each size to build. Its optimization problem is as follows:

MAX monthly earnings = 50 X1+20 X2

subject to

2 X1+4 X2<=400 (advertising budget available)

100 X1+50 X2<=8000 (Square footage required)

X1<=60 (rental limit expected)

X1,X2>=0

where

X1= Number of large spaces developed

X2= Number of small spaces developed

Question: The company is thinking about introducing a "medium storage space." Such a storage space would be 75 square feet, it would require no additional advertising and there would be no rental limit on it. What would have to be to the minimum contribution to the monthly earning from each medium space for the medium space to be viable?

Explanation / Answer

Since the shadow price of square footage is 0.4, minimum contribution to the monthly earning from each medium space for the medium space to be viable is 0.4

Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$2 Decision Variable X1 60 0 50 1E+30 10 $C$2 Decision Variable X2 40 0 20 5 20 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$7 Advertising budget 280 0 400 1E+30 120 $D$8 Square footage 8000 0.4 8000 1500 2000 $D$9 Rental limit expected 60 10 60 20 20

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