Exam 10: Nonlinear Programming

A firm has a cost function of 3x²- 25x + 374. Without having two examples of their output volume and total cost, we cannot determine their fixed cost.

The XYZ manufacturing company produces ball bearings. The annual fixed cost is $20,000 and the variable cost per ball bearing is $3. The price is related to demand according to the following equation: 1000 - 8p. -What is the optimal production quantity?

A profit function of Z = 3x² - 12x + 5 reaches maximum profit at x = 2 units of output.

Classical optimization uses calculus to determine the optimal values of a variable.

The XYZ manufacturing company produces ball bearings. The annual fixed cost is $20,000 and the variable cost per ball bearing is $3. The price is related to demand according to the following equation: 1000 - 8p. -What is the nonlinear profit function for the XYZ company? Simplify the terms as much as possible.

The first derivative of the fixed cost line is ________.

The first derivative of a cost function equals zero at the point V = 100. This is definitely the worst output volume for the producer to choose.

The XYZ manufacturing company produces ball bearings. The annual fixed cost is $20,000 and the variable cost per ball bearing is $3. The price is related to demand according to the following equation: V = 1000 - 8p. What is the optimal price of the ball bearings that will maximize the profit?

Both linear and nonlinear programming models are examples of

Sara's Sensible Critters makes two kinds of catnip toys: balls (x₁) and mice (x₂). The relationship between demand and price for balls and mice is: x₁ = 1800 - 150p₁ x₂ = 1500 - 300p₂ The cost for a catnip ball is $2 and for the mouse, $3. Sara has only 200 ounces of catnip on hand. A ball uses a tenth of an ounce and a toy mouse uses one-quarter of an ounce. -Write the appropriate expression for profit.

The ________ reflects the approximate change in the objective function resulting from a unit change in the quantity (right-hand-side) value of the constraint.

The XYZ manufacturing company produces ball bearings. The annual fixed cost is $20,000 and the variable cost per ball bearing is $3. The price is related to demand according to the following equation: 1000 - 8p. -What is the derivative of the profit function for the XYZ company? Simplify the terms as much as possible.

The ________ measure of distance between two points on a set of X and Y coordinates is the hypotenuse of a right triangle.

In solving the facility location problem, the objective is to locate a centralized facility that serves customers or other facilities such that the distance traveled between the facility and customers or other facilities is minimized.

The derivative of a function ________ the slope of the curve defined by that function.

Consider the curve 7x² - 14x + 28. What is the highest point on this curve?

Zoey's Catnip Toys faces the following relationship between price and demand: v = 2000 - 200p. The fixed cost is $500 and variable cost is $1. What price should Zoey charge to maximize profit?

Classical optimization is the use of ________ to determine the optimal value of a variable.

Consider the curve 7x² - 14x + 28. What is the slope at x = 5?

Classical optimization is the use of calculus to determine the optimal value of a variable.