3 0 3600 16 225 1200 16 16 3 0 the rectangle has a

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3= 0? =360016= 225𝐴′′= (1200 − 16?)= −163< 0The rectangle has a maximum area when x =225Find x = 225? = 600 − (43) 225 = 300b.. New Horizons Travel advertises a package plan for a Florida vacation. The fare forthe flight is $400/person plus $8/person for each unsold seat on the plane. Theplane holds 120 passengers and the flight will be cancelled if there are fewer than50 passengers. What number of passengers will maximize revenue?? = ?????? ?? ?????? ?????The dimensions of each rectangle has 200 meters and 225meters
560 − 16? = 0? = 35
𝑅′′= (560 − 16?)= −16 < 0The revenue will be maximum area when x =35Number of passengers = 120 -35 = 85c.An open-topped storage box with a square base has a capacity of 5 m3 . The materialfor the sides cost $1.60/m2 , while the material for the bottom costs $2.00/ m2 .Find the dimensions that will minimize the cost of making the box.The maximum revenue will be when the flight has 85passengers.
Unit # 4Extensions
𝐶= 4? −32?2C’= 04? −32?2= 04? =32?2?3= 8,? = 2𝐶′′= (4? −32?2) = 4 +64?3At x=2,?′′= 4 +6483= 12 > 0Cost is maximum when x=2At x =2 ,? =554= 1,25
Unit # 4Extensionsd.The perimeter of an isosceles triangle is 38 m. Find the length of the sides of thetriangle of maximum area.
Unit # 4ExtensionsWe know that the idosceles triangle is 38 meters? + ? + ? = 382? + ? = 38? = 38 − 2?From a triangle ABD,?2= ℎ2+ (?2)22= ?2− (19 − ?)22= 38? − 361ℎ = √38? − 361𝐴??? 𝐴 =12ℎ?𝐴??? 𝐴 = (12) (38 − 2?)√38? − 361𝐴??? 𝐴 = (19 − ?)√38? − 361𝐴= (( 19 − ?)√38? − 361)′𝐴= ( 19 − ?)12√38? − 361(38? − 361)+ √38? − 361(19? − ?)′𝐴=38(19 − ?)2√38? − 361− √38? − 361𝐴=316 − 19? − 38? + 361√38? − 361𝐴=722 − 57?√38? − 361Critical Numbers when Ais zero722 − 57?√38? − 361= 0
Unit # 4Extensions? =72257=38338? − 361 = 0? =36138=192𝐴′′= (722 − 57?√38? − 361)′𝐴′′=√38? − 361(722 − 57?)− (722 − 57?)(√38? − 361)′(√38? − 361)2𝐴′′=√38? − 361(−57) − (722 − 57?)(38√38? − 361)38? − 361𝐴′′=20577 − 27436(38? − 361)32𝐴′′=−6859(38? − 361)32When? =383, 𝐴′′=−6859(38?−361)32< 0The triangle has a maximum area when? =383When? =192, 𝐴′′=−6859(38(192)−361)32> 0The triangle has a minimum area when? =192
Unit # 4ExtensionsAt? =192,? = 38 − 2 (382) =383The length of the side of the triangle are383?,383? ,383?
Unit # 4Extensionse.An apple orchard now has 80 trees per hectare and the average yield is 400 applesper tree. For each additional tree planted per hectare the average yield per tree isreduced by approximately four apples. How many trees per hectare will give thelargest crop of apples?
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2 meters, 1 5 m s, New Horizons Travel, 1 5meters

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