LT $8$: I can solve and interpret an optimization problem in a real$-$world setting and discuss the application of elasticity in a given scenario.

The marketing team at Remi's Deli estimated that at a price of $p$ dollars for each turkey sandwich, the deli can expect to sell $q=-13p+250$ sandwiches each day. Which of the following statements accurately interprets the marketing team's analysis?

At a price of $$11\mathrm{.}49$ per sandwich, the demand is elastic. Raising the price per sandwich will decrease the total revenue.

At a price of $$9\mathrm{.}00$ per sandwich, the marginal revenue is $$53\mathrm{.}68.$

At a price of $$9\mathrm{.}00$ per sandwich, the demand is elastic. Raising the price per sandwich will decrease the total revenue.

At a price of $$11\mathrm{.}49$ per sandwich, the marginal revenue is $$16\mathrm{.}00.$