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{.}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

and

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

for

$,$

for

$.$

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:

$[$ Select $]$

and

$[$ Select $]$

for high$-$paying and low$-$paying markets, respectively, such that

$.$