Question

The I. Kruger Paint and Wallpaper Store is a large retail distributor of the Supertrex brand of vinyl wallcoverings. 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 demand 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 - (minus) 65,000 X Percentage markup taken above wholesale cost of a roll.

The store budgets a total of $17,000 for advertising, 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%. Kruger 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

Answer (a):

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

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

Answer (b):

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

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

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.