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Question : A company's cost for operating two warehouses is C(x, y) = 6x^2 + 4x + 12y^2 + 8y + 9, : 2151843

Solve the problem.

63) A company's cost for operating two warehouses is C(x, y) = 6x^{2} + 4x + 12y^{2} + 8y + 9, where x is the number of units in warehouse A and y is the number in B. Find the average cost to store a unit if A has 20 to 60 units, and B has 32 to 80 units.

A) $62,375

B) $47,034

C) $98,650

D) $89,560

64) A production function is given by P(x, y) = 300x^{2}y, where x is the number of units of labor and y is the number of units of capital. Find the average production level if x varies from 40 to 90 and y from 20 to 80.

A) 1,995,000,000

B) 399,000,000

C) 11,970,000,000

D) 66,500,000

65) A company's cost for operating two warehouses is C(x, y) = 4x^{3}y dollars, where x is the number of units in warehouse A and y is the number in B. Find the average cost to store a unit if A has 1 to 2 units, and B has 3 to 5 units.

A) $90

B) $60

C) $150

D) $120

66) A company's cost for operating two warehouses is C(x, y) = 6xy^{2} + 12x^{2}y + 4y dollars, where x is number of units in warehouse A and y is the number in B. Find the average cost to store a unit if A has 3 to 5 units, and B has 1 to 2 units.

A) $712

B) $359

C) $718

D) $356

67) Determine if the graph of the equation f(x, y) = 5x^{2} + 4y^{2} + 3 is a sphere, a hemisphere, a paraboloid, or none of these.

A) Sphere

B) Paraboloid

C) Hemisphere

D) None of these

68) Determine the type of curve given by vertical slices of the graph of the equation f(x, y) = 3x^{2} + 5y^{2} + 4.

A) Ellipse

B) Parabola

C) Circle

D) None of these

69) Determine the type of curve given by horizontal slices of the graph of the equation f(x, y) = 4x^{2} + 5y^{2} + 3.

A) Circle

B) Ellipse

C) Paraboloid

D) None of these

70) If a, b, and c are all nonzero, then determine if the plane ax + by + cz = 1 always intersects all three coordinate planes (i.e. the planes x = 0, y = 0, z = 0), sometimes intersects them, or never intersects them.

A) Sometimes

B) Always

C) Never

71) Determine if the graph of the equation f(x, y) = √(8 - x^{2} - y^{2}) is a sphere, a hemisphere, a paraboloid, or none of these.

A) Sphere

B) Hemisphere

C) Paraboloid

D) None of these

72) Determine if the graph of the equation x = 0 is a plane identical to, parallel to (but not identical to), or perpendicular to the yz-plane.

A) Perpendicular

B) Parallel

C) Identical

D) None of these

73) Determine which coordinate plane (i.e. xy-plane, yz-plane, or xz-plane) the graph of the equation y = -7 is parallel to.

A) xy-plane

B) xz-plane

C) yz-plane

Answer the question.

74) Given f(x,y) = x^{2} + y^{2}, the purpose of finding the critical points is which of the following?

(i) find local minima, if they exist

(ii) find local maxima, if they exist

(iii) find saddle points, if they exist

(iv) find interior points, if they exist

A) All are correct.

B) Only (i) and (ii) are correct.

C) (i), (ii), and (iii) are all correct.

D) Only (iii) is correct.

75) If (a,B) is a critical point in the interior of the domain of f(x,y) and if H = fxx(a,B) fyy(a,B) - [fxy(a,B) ]2, then f has a local minimum at (a,B) if

(i) H > 0 and fxx(a,B) > 0.

(ii) H > 0 and fxx(a,B) < 0.

(iii) H < 0.

A) Only (ii) is correct.

B) (i), (ii), and (iii) are all incorrect.

C) Only (iii) is correct.

D) Only (i) is correct.

76) If (a,B) is a critical point in the interior of the domain of f(x,y) and if D = fxx(a,B) fyy(a,B) - [fxy(a,B) ]2, then f has a local maximum at (a,B) if

(i) D > 0 and fxx(a,B) > 0.

(ii) D > 0 and fxx(a,B) = 0.

(iii) D < 0.

A) Only (iii) is correct.

B) Only (ii) is correct.

C) Only (i) is correct.

D) (i), (ii), and (iii) are all incorrect.

77) If (a,B) is a critical point in the interior of the domain of f(x,y) and if D = fxx(a,B) fyy(a,B) - [fxy(a,B) ]2, then f has a saddle point at (a,B) if

(i) D > 0 and fxx(a,B) > 0.

(ii) D > 0 and fxx(a,B) < 0.

(iii) D < 0.

A) Only (ii) is correct.

B) Only (iii) is correct.

C) Only (i) is correct.

D) None of the above is correct.

78) If we are looking for the critical points (a,B) on the surface of z = f(x,y), then we study the tangent lines to (a,B) along the slices parallel to the x-axis and y-axis. These tangent lines must have which of the following properties?

(i) They must be perpendicular.

(ii) They must be horizontal.

(iii) They must be horizontal, but not perpendicular.

(iv) They must be perpendicular, but not horizontal.

A) Only (iii) is correct.

B) Only (ii) is correct.

C) Only (iv) is correct.

D) Both (i) and (ii) are correct.

79) If we wish to locate the candidates for local extrema and saddle points in the interior of the domain of a function f(x,y), then how should we proceed?

(i) Set the partial derivatives equal to each other.

(ii) Set the partial derivatives equal to zero.

(iii) Set the partial derivatives equal to the critical values.

A) Only (iii) is correct.

B) Only (ii) is correct.

C) Only (i) is correct.

D) None of the above is correct.

80) If we wish to find the candidates for local extrema and saddle points for f(x,y) = x^{4}y + y^{3}x^{4}, then we must find which of the following?

(i) fx and fxx

(ii) f_{y} and f_{yy}

(iii) fxy

(iv) f_{yx}

(v) fxxx

A) (i) and (ii)

B) All

C) (i), (ii), and (v)

D) (i), (ii), and (iii)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

81) Write an "area" word problem for which finding the solution would involve evaluating the double integral

82) Write an "area" word problem for which finding the solution would involve evaluating the double integral

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

83) True or false? Consider the double integral

The first step in calculating this integral involves integrating with respect to y.

A) True

B) False

84) True or false? Consider the double integral

The first step in calculating this integral involves integrating with respect to x.

A) True

B) False

85) True or false? Consider the double integral

The first step in calculating this integral involves holding y constant.

A) True

B) False

86) True or false? Consider the double integral

The first step in calculating this integral involves holding y constant.

A) True

B) False

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

87) Write a "volume" word problem for which finding the solution would involve evaluating the double integral

88) Write a "volume" word problem for which finding the solution would involve evaluating the double integral