Questions from General Calculus

Q: The value of residential property for tax purposes is usually much lower

The value of residential property for tax purposes is usually much lower than its actual market value. If y is the market value, the assessed value for real estate taxes might be only 40% of y. Suppos...

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

Solve the exercise by the method of Lagrange multipliers. Find the values of x, y and z that minimize xy + xz - yz subject to the constraint x + y + z = 1.

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

Solve the exercise by the method of Lagrange multipliers. Find the values of x, y, and z that minimize xy + xz - 2yz subject to the constraint x + y + z = 2.

Q: Find the two positive numbers whose product is 25 and whose sum

Find the two positive numbers whose product is 25 and whose sum is as small as possible.

Q: Four hundred eighty dollars are available to fence in a rectangular garden

Four hundred eighty dollars are available to fence in a rectangular garden. The fencing for the north and south sides of the garden costs $10 per foot, and the fencing for the east and west sides cost...

Q: Three hundred square inches of material are available to construct an open

Three hundred square inches of material are available to construct an open rectangular box with a square base. Find the dimensions of the box that maximize the volume.

Q: The amount of space required by a particular firm is f (

The amount of space required by a particular firm is f (x, y) = 1000 √(6x2 + y2), where x and y are, respectively, the number of units of labor and capital utilized. Suppose that labor costs $480 per...

Q: Find the dimensions of the rectangle of maximum area that can be

Find the dimensions of the rectangle of maximum area that can be inscribed in the unit circle. [See Fig. 2(a).] Figure 2:

Q: Distance from a point to a parabola Find the point on the

Distance from a point to a parabola Find the point on the parabola y = x2 that has minimal distance from the point (16, ½). [See Fig. 2(b).] [Suggestion: If d denotes the distance from (x, y) to (16,...

Q: Suppose that a firm makes two products, A and B,

Suppose that a firm makes two products, A and B, that use the same raw materials. Given a fixed amount of raw materials and a fixed amount of labor, the firm must decide how much of its resources shou...