Question $3$

$2$ pts

Consider the La Strada restaurant problem above and assume that the cost of the lunch is $$4.$ Now assume that the restaurant classifies anybody with WTP more than $$7\mathrm{.}5$ as 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 to be less than or equal to $$1\mathrm{.}50$ in 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 $p_H^{**}-p_L^{**}1\mathrm{.}5.$