QUIZ 12
Math 1320-001
Friday. December 13
Name:
by writing my name I ssvear by the honor code
You have 10 minutes to complete this quiz. No notes. books or calculators are allowed.
1.
(1
2.
( points)
point)
i,rl-Iat
7
\
is the name for an N-dimensional triangle?
Use the method of Lagrange multipliers to set tip a system of equations for points
x, y, ) to check for maxima and minima for the objective function f(x, y) = 4x + 6
y subject to
constraint g(x, y)
2+y
x
2 13 = 0.
—
16J
3.
;
2
j
When using the method of Lagrange multipliers to minimize
+(y—1)
(x—3)
+
2
(z+1) subject to the constraint g(x,y,z) = 2
+y
r
+
z —4
we need to solve the following system of equations for x, y, z, ?:
(5
points)
f(xy,z)
=
0
3)
=
2xA
(1)
1)
=
2yA
(2)
2(z + 1)
=
2zA
(3)
=
4
(4)
2(u
—
—
+
+
2
z
Solve this system for x, y, z by solving the first three equations for x, y,
plugging them into the fourth equation.
2
=
z
in terms of ) and
2
9
>
4
(1
I
_i
L/
(‘1
):
ii:
_)
-
2
\4)
&ci
1
FJ
2
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2
\ a,e
7)
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