A street vendor constructs the table below on the basis of sales data. $($folel Consumer expenditure and revenue are terms for the same thing from different pariouctives. Corncier engende money that consumers spend on a product, and revenue is the amount of money that butinesses tale in by selling the product.$)$

Sales of Roses, Given the Price per Doaen

$\backslash$table$[[\backslash$table$[[$Price$],[($dollars$)]],\backslash$table$[[$Sales$],[($dogen roses$)]]],[20,164],[25,154],[30,129],[32,89]]$

$($a$)$ Find a quadratic function for the model of the data that gives the quantity sold at $x$ dollars, data from $20x32.($Round all numerical values to Evree secimal phans.$)S(x)=$

$($b$)$ Find a function for the model for consumer expenditure $($revenue for the vendor$),$ where $x$ is the price in dollars, daca from $20x32.($Round all numercar walues three onciR$(x)=$

$($c$)$ What price should the street vendor charge to maximiet consumer expenditure? $($Round your answer to two checimal places.$)$

$5$

$($C$)$ If aach daten roses costs the vendor $$15,$ what price should he charge to maximae his profit? $($Round your andwer to two decimal places.$)5$