Larson_Calculus_10e ch13sec10
MULTIPLE CHOICE
1. Use Lagrange multipliers to minimize the function subject to the following
constraint:
Assume that x and y are positive.
a.
b.
c.
d.
e.
no absolute minimum
2. Use Lagrange multipliers to find the maximum value of where and
subject to the constraint .
a.
b.
c.
d.
e.
3. Use Lagrange multipliers to maximize the function subject to the following
constraint.
Assume that x and y are positive.
a.
b.
c.
d.
e.
no absolute maximum
4. Use Lagrange multipliers to minimize the function subject to the following
constraint.
Assume that x, y, and z are positive.
a.
b.
c.
d.
e.
5. Use Lagrange multipliers to find the maximum value of where and
, subject to the constraint .
a.
b.
c.
d.
e.
6. Use Lagrange multipliers to find the maximum value of where
subject to the constraint .
a.
maxima: ; minima:
b.
maxima: ; minima:
c.
maxima: ; minima:
d.
maxima: ; minima:
e.
maxima: ; minima:
7. Use Lagrange multipliers to minimize the function subject to the
following two constraints.
Assume that x, y, and z are nonnegative.
a.
b.
c.
d.
e.
8. Use Lagrange multipliers to find the minimum distance from the line to the point
a.
b.
c.
d.
e.
9. Use Lagrange multipliers to find the minimum distance from the parabola to the point
. Round your answer to two decimal places.
a.
b.
c.
d.
e.
10. Use Lagrange multipliers to find the minimum distance from the circle to the point
. Round your answer to two decimal places.
a.
2.07
b.
c.
103.64
d.
10.18
e.
11. Use Lagrange multipliers to find the minimum distance from the plane to the point
. Round your answer to two decimal places.
a.
3.00
b.
c.
d.
9.81
e.
96.33
12. Find the highest point on the curve of intersection of the following surfaces.
Cone: , Plane:
a.
b.
c.
d.
e.
13. A cargo container (in the shape of a rectangular solid) must have a volume of 580 cubic feet. The
bottom will cost $6 per square foot to construct and the sides and the top will cost $4 per square foot to
construct. Use Lagrange multipliers to find the dimensions of the container of this volume that has
minimum cost.
a.
b.
c.
d.
e.
14. Let represent the temperature at each point on the sphere .
Find the maximum temperature on the curve formed by the intersection of the sphere and the plane
.
a.
b.
c.
d.
e.
15. Find the maximum production level if the total cost of labor (at $72 per unit) and
capital (at $40 per unit) is limited to $270,000, where x is the number of units of labor and y is the
number of units of capital. Round your answer to the nearest integer.
a.
42,016 units produced
b.
15,796 units produced
c.
29,115 units produced
d.
291,147 units produced
e.
19,792 units produced
16. Find the minimum cost of producing 55,000 units of a product , where x is the
number of units of labor (at $76 per unit) and y is the number of units of capital (at $56 per unit).
Round your answer to the nearest cent.
a.
$68,837.29
b.
$50,201.54
c.
$42,169.29
d.
$57,823.32
e.
$54,500.66