AGEC 3413 Chapter 10 Multiple Choice

If a firm's profit is Z = 12x - 6x2 + 30, and their minimum production level of x is equal to 0.5, then the level of x that maximizes profit is:

1.

Zevon Enterprises Which of these is the lawyer constraint for this scenario?

3X1 + 2X2 + 4X3 ≤ 5,000

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 - 200. 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?

5

Zevon Enterprises Which of these is the money constraint for this scenario?

6X1 + 4X2 + 7X3 ≤ 15,000

Zevon Enterprises The model is entered in Excel and the sensitivity report reveals that all of the constraints' Lagrange multipliers are zero. The impact for Zevon is:

Not all of the lawyers they have available will be used.

Zevon Enterprises The model is entered in Excel and executes to reveal that p2 equals $51.50. Which of these conclusions is correct?

The contribution to net profit from service X2 is $7,056.75.

Zevon Enterprises The model is entered in Excel and executes to reveal that p1 equals $45.57. Which of these conclusions is correct?

The demand for X1 is 97.

Salt Creek Soap Company What quantities of soap and shampoo maximize profit?

X1 = 0, X2 = 2

Salt Creek Soap Company What is profit when the optimal values of soap and shampoo are produced?

Z = 14

The slope of a curve at its highest point equals:

0.

A custom molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 - 5x1, and the per unit contribution for the cocktail glasses (x2) is 80 - 4x2. An expression for the total contribution is:

60x1 - 5x12 + 80x2 - 4x22.

Zevon Enterprises What is the best conclusion from the list below?

If Zevon can retain the services of another lawyer for less than $101, they should do so.

Sara's Sensible Critters Write the appropriate expression for profit.

Max Z = (p1 - 2)x1 + (p2 - 3)x2

Zevon Enterprises What is an appropriate objective function for this scenario?

Max Z = (p1 - 2.25)X1 + (p2 - 3)X2 + (p3 - 3.5)X3

The Lagrange multiplier is ________ to the dual variables in a linear programming problem.

analogous

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

calculus

Both linear and nonlinear programming models are examples of:

constrained optimization models.

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

equals

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

right-hand side

The Lagrange multiplier is:

the rate of change in the objective value as the RHS of the constraint increases.

Sara's Sensible Critters Write the appropriate expression for the demand constraint.

x1 = 2.5x2

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?

$63.99

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?

$9768