Consider the $La$ Strada restaurant problem above and assume that the cost $of$

the lunch $is$ $$5\mathrm{.}50.$ Now assume that the restaurant classifies anybody with $WTP$

more than $$7\mathrm{.}5as$ a high$-$paying customer; the rest are considered low$-$paying

customers. The restaurant will offer $la$ cart service $to$ high$-$paying customers

and a lunch buffet $to$ low$-$paying customers. $We$ again denote, $by{d}_H$ and $d_L,$

the demand for high$-$paying and low$-$paying customers, respectively. $It$ can $be$

shown that

$d_H(p)=125-10p$ for $7\mathrm{.}5p12\mathrm{.}5$

$d_L(p)=75-10p$ for $2\mathrm{.}5p7\mathrm{.}5$

The restaurant knows that the difference between the prices for the two

segments has $tobe$ less than $or$ equal $to$ $$1\mathrm{.}50in$ order $to$ effectively eliminate

cannibalization. $So,$ find the optimal prices:

$p_H^{*}=,$ and $p_L^{*}=$

for high$-$paying and low$-$paying markets, respectively, such that $p_H^{*}-p_L^{*}1\mathrm{.}5$