The i. kruger paint and wallpaper store

The I. Kruger Paint and Wallpaper Store is a large retail distributor of the Supertrex brand of vinyl wall-coverings. Kruger will enhance its citywide image in Miami if it can outsell other local stores in total number of rolls of Supertrex next year.  If is able to estimate the demand functions 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 marke-up taken above whole sale 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?