1-)Suppose that the labor cost for a building is approximated by C(x,y)=10x2+3y2?240x?180y+24,000 where x is the number of days of skilled labor and y is the number of days of semi-skilled labor required. Find the x and y that minimize cost C.

Ltfen birini sein:

x=18,y=90

x=12,y=30

x=18,y=18

x=30,y=18

x=24,y=60

2-)Use Lagrange multipliers to minimize f(x,y)=x2+y2?xy subject to x?y=10.

Ltfen birini sein:

f(10,0)=100

f(2,?1)=7

f(5,?5)=75

f(5,5)=25

f(1,2)=3

3-)Find dydx by using implicit differentiation for x3+3x2y+y3=8.

Ltfen birini sein:

dydx=?x2+2xyx2+y2

dydx=x2+6xyx2+3y2

dydx=?x2+3xyx2+y2

dydx=x2+3xyx2+y2

dydx=x2+2xyx2+y2

4-)

500 Ly 400+ 300- 200+ 100+ -10 -8 16 -4 -2/ 100- 2 4 6 18 10 X -200 + -300 -400 + -500+ Use the above given graph of y=f(x) to find the intervals where the function is increasing or decreasing