Question $3$

$2$ pts

Consider the La Strada restaurant problem above and assume that the cost of the lunch is $$6.$ Now assume that the restaurant classifies anybody with WTP more than $$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 and dy$,$ the demand for high$-$paying and low$-$paying customers, respectively. It can be shown that

d$($p$)=125-10$p for $7\mathrm{.}5<=$ p $<=12\mathrm{.}5,$

di $($p$)7510$p for $2\mathrm{.}5<=$ p $<7\mathrm{.}5.$

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:

$[$Select$]$

PH

and P

$[$Select$]$

for high$-$paying and low$-$paying markets, respectively, such that p$-$p$<=1\mathrm{.}5.$