Questions from General Calculus

Q: Find the possible values of x, y, z at which

Find the possible values of x, y, z at which f (x, y, z) = 5 + 8x - 4y + x2 + y2 + z2 assumes its minimum value.

Q: U.S. postal rules require that the length plus the

U.S. postal rules require that the length plus the girth of a package cannot exceed 84 inches. Find the dimensions of the rectangular package of greatest volume that can be mailed. [Note: From Fig. 5...

Q: Find the dimensions of the rectangular box of least surface area that

Find the dimensions of the rectangular box of least surface area that has a volume of 1000 cubic inches.

Q: A company manufactures and sells two products, I and II,

A company manufactures and sells two products, I and II, that sell for $10 and $9 per unit, respectively. The cost of producing x units of product I and y units of product II is 400 + 2x + 3y + .01(3...

Q: A monopolist manufactures and sells two competing products, I and II

A monopolist manufactures and sells two competing products, I and II, that cost $30 and $20 per unit, respectively, to produce. The revenue from marketing x units of product I and y units of product I...

Q: A company manufactures and sells two products, I and II,

A company manufactures and sells two products, I and II, that sell for $p1 and $p2 per unit, respectively. Let C(x, y) be the cost of producing x units of product I and y units of product II. Show tha...

Q: A company manufactures and sells two competing products, I and II

A company manufactures and sells two competing products, I and II, that cost $pI and $pII per unit, respectively, to produce. Let R(x, y) be the revenue from marketing x units of product I and y units...

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x2 - 3y2 + 4x + 6y + 8

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = ½ x2 + y2 - 3x + 2y - 5

Q: Solve the exercise by the method of Lagrange multipliers. Minimize

Solve the exercise by the method of Lagrange multipliers. Minimize ½ x2 - 3xy + y2 + 12, subject to the constraint 3x - y - 1 = 0.