Exam 10: Nonlinear Programming

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 optimal profit?

Assume price and demand are related by the following function: v = 200 - p. If fixed cost = $10,000 and variable cost = $8, then the expression for profit is ________.

Constraints for nonlinear programs are usually nonlinear.

The ________ of the value of investment is a measure of risk.

The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the ________ of the constraint equation.

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 formulation for this problem

Both linear and nonlinear programming models have the general form of an objective function subject to more than 1 constraint.

The objective of a facility location problem is to minimize ________.

The Salt Creek Soap Company has determined the following nonlinear model to determine the optimal pounds of industrial soap (X1) and shampoo (X2) it should produce each day. Maximize Z = X1² + 2X2² - 8X₁ - 12X₂ + 34 Subject to: X₁ + 2X₂ = 4 lbs -Determine the profit for the optimal production quantities of soap and shampoo.

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 profit?

Decision variables cannot be multiplied by each other in the objective function of a nonlinear program.

If price and demand are related by the function v = 15 + 15p and the fixed cost is $150 while the variable cost is $5, then the expression for profit is ________.

The Salt Creek Soap Company has determined the following nonlinear model to determine the optimal pounds of industrial soap (X1) and shampoo (X2) it should produce each day. Maximize Z = X1² + 2X2² - 8X1 - 12X₂ + 34 Subject to: X₁ + 2X₂ = 4 lbs -What is profit when the optimal values of soap and shampoo are produced?

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 the demand constraint.

In an unconstrained nonlinear programming problem, we have a single nonlinear objective function and no constraints..

The ________ the variability in an investment portfolio, the ________ the risk of the investment portfolio.

Both linear and nonlinear programming models are examples of constrained optimization models.

If a firm's profit is Z = 20p -2p² + 40, then the optimal value of I yields a maximum profit of ________.

A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x² - 10C² + 40Cx + 120x - 200C + 600. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales?

The dual value of a resource in a nonlinear programming model is given by the ________.