$1.$ A startup coffee shop has determined that the demand function for their coffee is $18,000-($P $-5)/1\mathrm{.}16*700,$ where P is the price. What price should they set to maximize the revenue?

$2.$ #no option, NPV

A startup firm is considering building a ski resort in a state that plans to construct a new airport to attract more tourists.

The state will announce in one year whether the airport plan is approved in the state budget, and the construction is expected to take three years to complete.

$($we assume that once the plan is approved, the airport will be built successfully$).$

It takes threes years to build the hotel and the firm wants to hotel to be ready when the new airport is put into operation.

Projected Annual Cash Outflow to Build The Hotel Over $3-$Years:

In $1-$Year: Legal documents preparation, Build foundation $$2$

In $2-$Years: Main construction $$2$

In $3-$Years: Finishing $$1$

Projected Present Value from Operating the Hotel in Two Scenarios

Scenario #$1$: Good Case: The airport plan passes the state budget and the airport is built: $$26.$

Scenario #$2$: Bad Case: The airport plan fails to pass the state budget: $$4.$

For simplicity, let$$s assume that the discount rate is $0\%.$ The firm doesn't have the option to quit. Once they start the project in year $1,$ they must finish the project.

The consulting team predicts that the probability the airport plan passes the state budget is $0\mathrm{.}5.$

What is the NPV $($the revenue minuses the cost$)$ of the project?