Ch $8$ Hw Answers

Q$.8$:$8-11($Pricing and marketing strategy problem$)$ The I. Kruger Paint and Wallpaper Store is a large retail distributor of the Supertrex brand of vinyl wallcoverings. Kruger will enhance its citywide image in Miami if it can sell more rolls of Supertrex next year than other localustores. It is able to estimate the demand function as follows:

Number of rolls of Supertrex sold $=20$ Dollars spent on advertising $+6\mathrm{.}8$ Dollars spent on in$-$store displays $+12$ Dollars invested in on$-$hand wallpaper inventory $-65,000$ 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?

$8-11.$ Maximize number of rolls of Supertrex sold $=20x_1+6\mathrm{.}8x_2+12x_3-65,000x_4$ where

$x_1=$ dollars spent $on$ advertising

$x_2=$ dollars spent $on$ store displays

$x_3=$ dollars $in$ inventory

$x_4=$ percent markup

subject to