Asmall cruising ship that can hold up to 66 people provides three-day excursions to groups of 42 or more. if the group contains 42 people, each person pays $64. the cost per person for all members of the party is reduced by $1 for each person in excess of 42. find the size of the group that maximizes income for the owners of the ship.

size of group is 53 people

Explanation:

given data

person = 42

per person pay = $64

to find out

size of the group that maximizes income for the owners of the ship

solution

we will consider here number of additional person is = x

so

total passenger =  x + 42

and price per person = 64 - x

so

total income is

R ( x) = ( x + 42 ) × ( 64 - x )

R ( x) = −x² + 22 x + 2688    .......................1

and maximize the total income will be when R (x) is a quadratic function

so

f (x) = ax² + bx + c is maximum

when a ≤ 0 and x =

so

income will maximum when  x from equation  1

x =  

x = 11

so

size of group is 42 + 11 = 53

steering wheels are always situated on the left side of the car.

always drive on the right side of the road.

white lines separate lanes of traffic traveling the same direction.

hashed or broken lines means you may change lanes when it is safe.

solid white lines mean stay in your lane.

yellow lines separate traffic moving in opposing directions.

hashed or broken yellow lines mean you can carefully pass, paying attention to oncoming traffic.

never cross a solid yellow line (or double yellow line).

when turning left at an intersection, pass in front of any cars that are turning left from the opposing direction (do not try to pass behind them).

use the left lane to pass other cars traveling your direction.

do not pass in the right lane unless absolutely necessary.

if you are driving in the far left hand lane and someone would like to pass you, move over to the right lane when it is safe to do so and allow them to pass.

you must always yield to pedestrians.

come to a complete stop whenever you see pedestrians trying to cross the street.

never pass a school bus if it has flashing red lights. wait until the lights have stopped.

be aware of bicyclists. often they share the road with cars and are supposed to also follow general traffic laws.

be particularly careful about driving in cities with bike lanes -- always check before turning that a bike is not coming.

it is mandatory to pull over or stop at an intersection to allow an emergency vehicle to pass you if you see one traveling with lights flashing and/or a siren running.

do not overuse your car horn. horns are used almost exclusively for emergency situations or for when you feel unsafe.

explanation: