6. The LP model and output below represent a problem whose solution will tell a
ID: 3367431 • Letter: 6
Question
6. The LP model and output below 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 so variables measure the number of women's (XI), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units, special display racks, demand, and a marketing restriction, respectively. ld. The MAX 4 X1 6 X2 +5 X3 +3.5 X4 SUBJECT TO 2) 2 XI +3 X2+3 X3 + X4120 3) 1.5X1+2X2Explanation / Answer
Solution
Back-up Concepts
Of the three images provided in the question,
the first (topmost) shows the objective function and constraints (numbered 2 to 5)…….(1)
the second (middle) shows the solution output ……………………………………………(2)
the third (bottom most) gives the questions to be answered.
Now, the answers,
(a) to (d): refer to image 2 which shows the 4 variables, X1, X2, X3 and X4 against each the value given is the solution. Thus,
(a) X1 = 12 => 12 women’s umbrellas must be produced. ANSWER 1
(b) X2 = 0 => No golf umbrellas must be produced. ANSWER 2
(c) X3 = 12 => 12 men’s umbrellas must be produced. ANSWER 3
(d) X4 = 60 => 60 folding umbrellas must be produced. ANSWER 4
(e) to (g): refer to image 2 rows 2, 3, 4, 5 and the slack or surplus values given against these rows. Thus,
(e) Row 2 pertains to storage space. Against that, value given is 0. => no space is left unused. ANSWER 5
(f) Row 3 pertains to special display racks. Against that, value given is 36. => 36 racks are left unused. => only 18 are used. ANSWER 6 [refer to first image row 3 right hand says 54 which indicates the number of racks available.]
(g) Row 5 pertains to marketing restriction. Against that, value given is 0. => no marketing restriction is exceeded. ANSWER 7
(h) Refer to the top of Image 2 where the objective function value is shown as 318. This gives the maximum profit. ANSWER 8
DONE
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