The LP model and LINDO output represent a problem whose solution will tell a spe

ID: 347252 • Letter: T

Question

The LP model and LINDO output represent a problem whose solution will tell a specialty retailier 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, gott, men's, and folding umbrelas respectively. The constraints measure storage space in units, special display racks, demand, and a marketing restriction, respectively MAX 4 X1+6X2 5 X3+3.5 X4 SUBJECT TO 2) 2x1 + 3x2 + 3x3 + x4 3) 1.5X1+2 X2 54 4) 2x2 + x3 + x4

Explanation / Answer

a) 12

(table 1: value of variable X1(representing women's umbrella)=12, hence, 12 women's umbrellas should be stocked)

b)0

Table 1:value of X2

c)12

Table 1:value of X3

d)60

Table 1:value of X4

e)0

Table2:slack or surplus for Row (2)

f)18

Table2: RHS of Constraint (3)=54- row (3) surplus=36, 54-36=18

g)0

Table 2: slack for Row (5)

h) 318

Objective function value

i) 1

Table 3: allowable increase of variable X1

j) 6.5

Table 3: allowable increase of variable X2=0.5, current coefficient=6, profit from golf umbrellas can increase up to=6+0.5

k) 48

Table 4: allowable increase for space constraint row (2)

l)yes

Dual price for demand constraint = 1.5, hence, the total increase in profit will be = 1.5*(86-72) = 21, giving us a net benefit of 21-$20 cost=$1.