Peery White wants to create a fenced- in, Rectangular rose garden adjacent to hi

Question

Peery White wants to create a fenced- in, Rectangular rose garden adjacent to his (straight) driveway. Tha plan is to build a low fence along the driveway (costing $0.50 per foot) and a higher fence on the other three sides (costing $2 pear foot) If the area of the garden is to be 1440 square feet, find the dimensions which will minimize the cost of the fence. A certain vintage wine appreciates in valve each year, but there are also annual storage valve (per case) of the wine t years after it is bottled is estimate to be v(t) = 450 + 18 squareroot t - 2t dollars (0 lessthanequal to t lessthanequal to 60) After now many years will the case of wine attain its maximum value What is that maximum value

Explanation / Answer

a)let length of low fence =x

legth of side adjacent to low fence =y

iven low fence cost 0.5$ per foot , highesr fence cost 2$ per foot

total cost of fence C=0.5x +2(x+y+y)

C=2.5x +4y

area of garden =1440 sq ft

Area =A= xy =1440

y=1440/x

cost C=2.5x + 4*(1440/x)

for minimum cost of fence dC/dx =0 ,d2C/dx2>0

dC/dx=2.5 - 4*(1440/x2) =0

x2=4*1440/2.5

x=48

,d2C/dx2=4*(1440*2/x3) >0

x=48

y=1440/48

y=30

dimensions that minimise cost are low fence =48ft , other 3 sides =30 feet each

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