Question

3. Find nonnegative numbers x and y, x+y=90, such that xy is maximized. 4. (Revenue) A local club is arranging a charter flight to Hawaii. The cost of the trip is $1600 each for 90 passengers, with a refund of $10 per passenger for each passenger in excess of 90. (a) Find the number of passengers that will maximize the revenue received from the flight. (b) Find the maximum revenue.

Answer 1

Comment in case of any doubt.

= 9021²_W Let 3 azy 942 (90-01) 90-11 flou- gon²_n = f'(o)= 90 (22) - 30² 3712 - => 301 ( 60 - 0) = 0 => 0 = 0,60 f"(a) = 180 at r1=0 on 80, For marimum, f'(o)=0 and f" (1)<0, this at a=60. Then Thus, 21 = 60 and y = 30 L 100-400) 180 af x=80 occurs y = 90-60= 30 = 4Q) Revenue, Rlor) (1600-100)(90+81) → Rín)= -10690+1) Total passengers price..cost per +1600-1001/1) passenger = 700-20.30 (for critical points) =) = 35 R" (01) marimum of RLM) at 01=35 so, number of passengers that manimize revenue 907 35= (b) (1600- 350) (125) = 1250x125 = $ 156250 Thus, maximum avenue is 1$ 156,250 = -10-10= -20 < 0 so 125 Ramarimum