Problem $4(27$ points$)$: Pricing and Marketing Strategy

The PW store is a large retail distributor of the WOW brand of vinyl wall coverings. PW will

enhance its citywide image in Vancouver if it can outsell other local stores in total number of

rolls of WOW next year. It is able to estimate the demand function $($i$.$e$.$ objective function$)$ as

follows: $$

Number rolls of WOW sold $={20}^{*}$ dollars spent on advertising $+{6\mathrm{.}8}^{*}$ dollars spent on in$-$store

displays $+{12}^{*}$ dollars invested in on$-$hand wallpaper inventory $-75,{000}^{*}$ percentage markup

taken above wholesale cost of a roll.

For example: $$

If $$8000$ dollars is spent on advertising then the impact will be $20*8000=160,000$ rolls

of WOW sold.

If the percentage markup is $40\%$ then this will reduce$/$decrease the number of WOW

sold by $75,{000}^{*}0\mathrm{.}4=30,000$ rolls.

The store budgets a total of $$34,000$ for advertising, in$-$store displays and on$-$hand inventory

$($i$.$e$.$ stock$)$ of WOW wallpaper for next year. It decides it must spend at least $$6,000$ on

advertising; in addition, at least $5\%$ of the amount invested in on$-$hand inventory $($i$.$e$.$ stock$)$

should be devoted to displays.

Markups on WOW seen at other local stores range from $30\%$ to $55\%.$ PW decides that its

markup had best be in this range as well.

a$.$ Formulate algebraically a Linear Programming model for this problem. The objective

is to maximize the number of rolls of WOW sold. $(14$ points$).$

b$.$ Formulate this same linear programming problem on a spreadsheet and SOLVE using

Excel Solver $($Provide the corresponding "Excel Spreadsheet" and the "Answer

Report"$).$ Include "managerial statements" that communicate the results of the

analyses. $($i$.$e$.,$ describe verbally$/$narratively the results$).(9$ points$)$

c$.$ What is the difficulty with the answer of the optimal solution? What constraint would

you add? $(4$ points$).$