Question

2:8-11 (Pricing and marketing strategy problem) The I. Kruger Paint and Wallpaper Store is a large retail distributor of the Supertrex brand of vinyl wallcov- erings. Kruger will enhance its citywide image in Miami if it can sell more rolls of Supertrex next year than other local stores. It is able to estimate the de- mand function as follows: Number of rolls of Supertrex sold = 20 X Dollars spent on advertising + 6.8 X Dollars spent on in-store displays + 12 x Dollars invested in on-hand wallpaper inventory – 65,000 X Percentage markup taken above wholesale cost of a roll The store budgets a total of $17,000 for adver- tising, in-store displays, and on-hand inventory of Supertrex for next year. It decides it must spend at least $3,000 on advertising; in addition, at least 5% of the amount invested in on-hand inventory should be devoted to displays. Markups on Supertrex seen at other local stores range from 20% to 45%. Kru- ger decides that its markup had best be in this range as well. (a) Formulate as an LP problem. (b) Solve the problem. (c) What is the difficulty with the answer? (d) What constraint would you add?

Answer 1

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Answer (a):

Let us consider the folliwng variable as inputs for the given data,

x, =Dollars spent on advertising X, =Dolars spent on in-store displays X, =Dollars invesled in on-hand wallpaper inventory X, = Percentage markup taken above wholesale cost of a roll

We have the total budget for advertising & other expenses is $17,000

Thus we formulate a LPP based on the given constraints to maximize demand

Maximize demand = 20X, +68X, +12X, - 65,000X, Subject to %3D X,+X,+X,<17,000 Budget for the three methods X, 23,000 At least 3,000 for advertsing At least 5% of inventory for displays X, 2 5%X,

Answer (b):

We use QM for windows which is a mathematical analysis tool for Management Science by inputting all the constrains above,

Linear Programming Results 8-11 Solution X1 X2 X3 X4 RHS Maximize 20 6.8 12 -65000 17000 Constraint 1 Constraint 2 3000 Constraint 3 -.05 Constraint 4 .45 Constraint 5 .2 Solution-> 17000 .2 327000

Ranging 8-11 Solution Reduced Cost Value Variable Original Val Lower Bound Upper Bound |х1 х2 17000 20 11.7524 Infinity -In finity 6.8 20 X3 -In finity 8.66 12 20.66 X4 -In finity .2 -65000 Dual Value Constraint Slack/Surplus Original Val Lower Bound Upper Bound 17000 3000 Infinity Constraint 1 20 -In finity Constraint 2 14000 3000 17000 Constraint 3 -13.2 14000 Constraint 4 .25 .45 .2 Infinity Constraint 5 -65000 .2 .45

We find the optimal solution as => X1 = 17,000 X2 = 0 X3 = 0 & X4 = 0.2

By using all the values in the earlier LPP formulated, we get the maximum demand as

Maximize demand = 20X, +68X,+12X, - 65,000X, = 20x17,000 – 65,000x 02 327,000

Answer (c):

From the given above ideal solution, it very well may be examined that no dollars are spent on in-store shows and close by stock. Anyway notice that, on the off chance that we don't have both these promoting strategies, it may be difficult to sell the item. Henceforth the ideal arrangement is some way or another impossible.

Answer (d):

I will prescribe including an imperative that at any rate a particular measure of backdrop ought to be close by stock.