The LP model and LINDO output represent a problem whose solution will tell a specialty retailer how many of four different styles…
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Question:
The LP model and LINDO output represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women’s, golf, men’s, and folding umbrellas, respectively. The constraints measure storage space in units, special display racks, demand, and a marketing restriction, respectively.
MAX 4 X1 + 6 X2 + 5 X3 + 3.5 X4
SUBJECT TO
2) 2 X1 + 3 X2 + 3 X3 + X4 <= 120  
3) 1.5 X1 + 2 X2 <= 54  
4) 2 X2 + X3 + X4 <= 72  
5) X2 + X3 >= 12 
END
OBJECTIVE FUNCTION VALUE
1) 318.00000
VARIABLE  VALUE  REDUCED COST 
X1  12.000000  .000000 
X2  .000000  .500000 
X3  12.000000  .000000 
X4  60.000000  .000000 
ROW  SLACK OR SURPLUS  DUAL PRICE 
2)  .000000  2.000000 
3)  36.000000  .000000 
4)  .000000  1.500000 
5)  .000000  2.500000 
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ. COEFFICIENT RANGES  
VARIABLE  CURRENT COEFFICIENT 
ALLOWABLE INCREASE 
ALLOWABLE DECREASE 
X1  4.000000  1.000000  2.500000 
X2  6.000000  .500000  INFINITY 
X3  5.000000  2.500000  .500000 
X4  3.500000  INFINITY  .500000 

RIGHT HAND SIDE RANGES  
ROW  CURRENT RHS 
ALLOWABLE INCREASE 
ALLOWABLE DECREASE 
2  120.000000  48.000000  24.000000 
3  54.000000  INFINITY  36.000000 
4  72.000000  24.000000  48.000000 
5  12.000000  12.000000  12.000000 
Use the output to answer the questions:
a.  How many women’s umbrellas should be stocked? 
b.  How many golf umbrellas should be stocked? 
c.  How many men’s umbrellas should be stocked? 
d.  How many folding umbrellas should be stocked? 
e.  How much space is left unused? 
f.  How many racks are used? 
g.  By how much is the marketing restriction exceeded? 
h.  What is the total profit? 
i.  By how much can the profit on women’s umbrellas increase before the solution would change? 
j.  To what value can the profit on golf umbrellas increase before the solution would change? 
k.  By how much can the amount of space increase before there is a change in the dual price? 
l.  You are offered an advertisement that should increase the demand constraint from 72 to 86 for a total cost of $20. Would you say yes or no? 
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