Larson_Calculus_10e ch13sec09
MULTIPLE CHOICE
1. Find the minimum distance from the point to the plane .
a.
b.
c.
d.
e.
2. Find the minimum distance from the point to the surface .
a.
b.
c.
d.
e.
3. Find three positive numbers x, y, and z whose sum is 24 and product is a maximum.
a.
b.
c.
d.
e.
429
415
55
607
3 7
4. Find three positive numbers x, y, and z whose sum is 30 and the sum of the squares is a minimum.
a.
b.
c.
d.
e.
5. Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The
volume of the room is 640 cubic feet. The cost of wall paint is $0.076 per square foot and the cost of
ceiling paint is $0.19 per square foot. Let x, y, and z be the length, width, and height of a rectangular
room respectively. Find the room dimensions that result in a minimum cost for the paint. Round your
answers to two decimal places.
a.
b.
c.
d.
e.
6. Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The
volume of the room is 360 cubic feet. The cost of wall paint is $0.054 per square foot and the cost of
ceiling paint is $0.18 per square foot. Let x, y, and z be the length, width, and height of a rectangular
room respectively. Identify the room dimensions that result in a minimum cost for the paint and use
these dimensions to find the minimum cost for the paint. Round your answer to the nearest cent.
a.
$54.00
b.
$8.64
c.
$7.00
d.
$19.44
e.
$21.60
7. The material for constructing the base of an open box costs 1.5 times as much per unit area as the
material for constructing the sides. For a fixed amount of money $150.00, find the dimensions of the
box of largest volume that can be made.
a.
b.
c.
d.
e.
8. Suppose a trough with trapezoidal cross sections is formed by turning up the edges of a 30-inch-wide
sheet of aluminum (see figure). Find the cross section of maximum area.
a.
b.
c.
d.
e.
9. A company manufactures two types of sneakers: running shoes and basketball shoes. The total revenue
from units of running shoes and units of basketball shoes is:
,
where and are in thousands of units. Find and so as to maximize the revenue.
a.
b.
c.
d.
e.
10. Suppose a corporation manufactures candles at two locations. The cost of producing units at
location 1 is and the cost of producing units at location 2 is
. The candles sell for $43 per unit. Find the quantity that should be produced
at each location to maximize the profit .
a.
b.
c.
d.
e.
11. Find the least squares regression line for the points shown in the graph.
a.
b.
c.
d.
e.
12. The least squares regression line for the points shown in the graph is . Calculate S, the
sum of the squared errors.
a.
b.
c.
d.
e.
13. Find the least squares regression line for the points .
a.
b.
c.
d.
e.
14. Find the least squares regression line for the points .
Round numerical values in your answer to two decimal places.
a.
b.
c.
d.
e.
15. Find three positive numbers x, y, and z whose sum is 48 and is a maximum.
a.
x = 10, y = 7, z = 31
b.
x = 7, y = 31, z = 10
c.
x = 31, y = 10, z = 7
d.
x = 12, y = 24, z = 12
e.
x = 12, y = 12, z = 24