"You are responsible for constructing a new building. The building will have 9 floors. You are considering modifying the design of the structure with extra steel, utilities, and elevator shafts so that it will be easier to double the height of the building to 18 floors (after the building is constructed). You need to decide whether to modify the design of the building before the building is constructed. When the building is built with 9 floors, there will either be 9 occupants or 5 occupants. There is a 0.73 probability that there will be 9 occupants. If there are 5 occupants, your company will never choose to make the building taller. If there are 9 occupants, your company may decide to double the height of the building (to 18 floors). There is a 0.35 probability the building will have 18 total occupants and a 0.65 probability the building will have 14 total occupants. The revenue for the company depends on the number of occupants in the building: the revenue for 5, 9, 14, and 18 occupants is $5, $9, $14, and $18, respectively. NOTE: If there are originally 9 occupants and the building's height is doubled, assume the revenue of the company is either $14 or $18 . DO NOT ADD $9 +$14 or $9 +$18. The cost for the company depends on whether the design is modified and whether it chooses to double the height of the building. The cost to modify and double the height is $10. The cost to modify the building and not double its height is $5. The cost to double the height without modifying the design is $11. The cost of neither modifying or doubling the height is $3. Your company wants to maximize its expected profit (where profit is the revenue gained from the occupants minus the cost). What is the expected profit for the optimal option, rounded to the nearest tenth of a dollar? This includes whether or not to modify the design and wether or not to double the height."