Questions from General Calculus

Q: A firm makes x units of product A and y units of

A firm makes x units of product A and y units of product B and has a production possibilities curve given by the equation 4x2 + 25y2 = 50,000 for x ≥ 0, y ≥ 0. (See Exercise 23.) Suppose profits are $...

Q: Let f (r, y, x) be the real

Let f (r, y, x) be the real estate tax function of Exercise 13. (a) Determine the real estate tax on a property valued at $100,000 with a homeowner’s exemption of $5000, assuming a tax rate of $2.20 p...

Q: The production function for a firm is f (x, y

The production function for a firm is f (x, y) = 64 x3/4 y1/4, where x and y are the number of units of labor and capital utilized. Suppose that labor costs $96 per unit and capital costs $162 per uni...

Q: Consider the firm of Example 2, Section 7.3,

Consider the firm of Example 2, Section 7.3, that sells its goods in two countries. Suppose that the firm must set the same price in each country. That is, 97 - (x/10) = 83 - (y/20). Find the values o...

Q: Find the values of x, y, and z that maximize

Find the values of x, y, and z that maximize xyz subject to the constraint 36 - x - 6y - 3z = 0.

Q: Find the values of x, y, and z that maximize

Find the values of x, y, and z that maximize xy + 3xz + 3yz subject to the constraint 9 - xyz = 0.

Q: Find the values of x, y, z that maximize 3x

Find the values of x, y, z that maximize 3x + 5y + z - x2 - y2 - z2, subject to the constraint 6 - x - y - z = 0.

Q: Find the values of x, y, z that minimize x2

Find the values of x, y, z that minimize x2 + y2 + z2 - 3x - 5y - z, subject to the constraint 20 - 2x - y - z = 0.

Q: The material for a closed rectangular box costs $2 per square

The material for a closed rectangular box costs $2 per square foot for the top and $1 per square foot for the sides and bottom. Using Lagrange multipliers, find the dimensions for which the volume of...

Q: Use Lagrange multipliers to find the three positive numbers whose sum is

Use Lagrange multipliers to find the three positive numbers whose sum is 15 and whose product is as large as possible.