9. 4 points TanApCalc10 44.0 57 My Notes Ask Your Teacher The quantity demanded

Question

9. 4 points TanApCalc10 44.0 57 My Notes Ask Your Teacher The quantity demanded each month of the sicard sports watch is related to the unit price by the equation ??0.01r +1 OS S 20) where ? s measured n dolars and x s measured in units o a thousand. T yield a maximum revenue, how many watches must be sold? ound your answer t the nearest whole number. watches Need Help? 10. 3 points TankpCalc10 4 5.003. My Notes Ask Your Teacher enclose a The owner of the Rancho Grande has 2988 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river Ir fencing is not required along the river, what are the dimensions of the largest area he can enclosc? shorter side yd onger side yd What is this area? yd2

Explanation / Answer

Solution:- Let y = the length along the river
Let x = distance from river to fence parallel to the river (shorter side)
given that y + 2x = 2988 that is y = 2988 - 2x
Also the Area = A = x * y
A (x) = x * (2988 - 2x)
A(x) = 2988x - 2x^2 ------------------------------(i)
for critical number put A'(x) = 0
Now A'(x) = 2988 - 4x
2988 - 4x = 0 so x = 2988 / 4 = 747 yd
and y = 2988 - 2x
y = 2988 - 2 * 747 = 1494 yd

Further Using swcond derivative test we can show that A''(x) =-2 <0 so A(x) is maximum at x=747

Maximum Area A = 1494 * 747 = 1116018 yd^2

shorter side =747 yd

and longer side = 1494 yd

A(max) = 756 * 1512 = 1,143,072 square yards

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