Question 1

A function of one argument is maximized when the first derivative:

Accepted Answer

A)  is zero and the second derivative is positive. 
B)  is positive and the second derivative is negative. 
C)  is zero and the second derivative is negative. 
D)  is negative and the second derivative is positive. 
E)  and the second derivative are both zero. 
A)  is zero and the second derivative is positive. 
B)  is positive and the second derivative is negative. 
C)  is zero and the second derivative is negative. 
D)  is negative and the second derivative is positive. 
E)  and the second derivative are both zero.

Question 2

Fox's Fine Furs (FFF)estimates that its total cost of production is TC = 125 + 100Q + 25Q2.Furs sell for $1,100 each.To maximize profits,FFF should sell:

Accepted Answer

A)  8 furs. 
B)  no furs. 
C)  20 furs. 
D)  38 furs. 
E)  22 furs. 
A)  8 furs. 
B)  no furs. 
C)  20 furs. 
D)  38 furs. 
E)  22 furs.

Question 3

If Y = 3 / X,then d2Y/dX 2 is:

Accepted Answer

A)  -6 / X 3. 
B)  -3 / X 2. 
C)  6 / X 2. 
D)  6 / X 3. 
E)  6X 3. 
A)  -6 / X 3. 
B)  -3 / X 2. 
C)  6 / X 2. 
D)  6 / X 3. 
E)  6X 3.

Question 4

Murdock Glass sells stained glass panes.Its profit is given by p = -500 + 100X - X2.The profit-maximizing level of output is:

Accepted Answer

A)  X = 50. 
B)  X = 100. 
C)  X = 200. 
D)  X = 300. 
E)  X = 600. 
A)  X = 50. 
B)  X = 100. 
C)  X = 200. 
D)  X = 300. 
E)  X = 600.

Question 5

If Y = X3(5 + X 2)4,then dY/dX is:

Accepted Answer

A)  3X 2(5 + X 2)4 + 8X3(5 + X 2)3. 
B)  3X 2(5 + X 2)4 + 8X4(X 2)3. 
C)  3X 2(5 + X 2)3. 
D)  3X 2(5 + X 2)4 + 8X4(5 + X 2)3. 
E)  3X 2(5 + X 2)4 + 8X4(5 + X 2)2. 
A)  3X 2(5 + X 2)4 + 8X3(5 + X 2)3. 
B)  3X 2(5 + X 2)4 + 8X4(X 2)3. 
C)  3X 2(5 + X 2)3. 
D)  3X 2(5 + X 2)4 + 8X4(5 + X 2)3. 
E)  3X 2(5 + X 2)4 + 8X4(5 + X 2)2.

Question 6

Shag Express,a retailer of lamps,has determined that its total cost of retailing lamps is TC = 200 + 10Q + 5Q2.At 10 units of output,the firm's marginal cost is:

Accepted Answer

A)  $110. 
B)  $100. 
C)  $800. 
D)  $230. 
E)  $10. 
A)  $110. 
B)  $100. 
C)  $800. 
D)  $230. 
E)  $10.

Question 7

NotAlligator Briefcases estimates that its total cost of producing vinyl bags is TC = 65 + 9 / Q + 5Q2.At 3 units of output,NotAlligator's marginal cost is:

Accepted Answer

A)  $113. 
B)  $29. 
C)  $27. 
D)  $119. 
E)  $9. 
A)  $113. 
B)  $29. 
C)  $27. 
D)  $119. 
E)  $9.

Question 8

Campbell's sells used trailers,U,and new trailers,N.Its profits are given by p = 100N + 68U - 5N2 - 5U2 - 2NU.Campbell's maximum profit is:

Accepted Answer

A)  $455. 
B)  $588. 
C)  $620. 
D)  $495. 
E)  $640. 
A)  $455. 
B)  $588. 
C)  $620. 
D)  $495. 
E)  $640.

Question 9

If Y = -2 + X + 32X3,then dY/dX is:

Accepted Answer

A)  1 + 96X3. 
B)  -1 + 96X2. 
C)  1 + 96X2. 
D)  96X2. 
E)  X + 32X3. 
A)  1 + 96X3. 
B)  -1 + 96X2. 
C)  1 + 96X2. 
D)  96X2. 
E)  X + 32X3.

Question 10

If Y = U(X)W(X),then dY/dX is:

Accepted Answer

A)  U dW/dX - W dU/dX. 
B)  U dW/dX + W dU/dX. 
C)  (W dW/dX) / (U dU/dX). 
D)  (U dW/dX)(W dU/dX). 
E)  W dW/dX + U dU/dX. 
A)  U dW/dX - W dU/dX. 
B)  U dW/dX + W dU/dX. 
C)  (W dW/dX) / (U dU/dX). 
D)  (U dW/dX)(W dU/dX). 
E)  W dW/dX + U dU/dX.

Question 11

The second derivative of the total profit function is:

Accepted Answer

A)  average profit. 
B)  marginal profit. 
C)  the slope of the average profit function. 
D)  the slope of the marginal profit function. 
E)  the slope of the total profit function. 
A)  average profit. 
B)  marginal profit. 
C)  the slope of the average profit function. 
D)  the slope of the marginal profit function. 
E)  the slope of the total profit function.

Question 12

The first derivative of total profit with respect to quantity is:

Accepted Answer

A)  average revenue. 
B)  marginal revenue. 
C)  marginal profit. 
D)  average profit. 
E)  total profit. 
A)  average revenue. 
B)  marginal revenue. 
C)  marginal profit. 
D)  average profit. 
E)  total profit.

Question 13

If Y = 12 - 6X + 8X -1/2,then dY/dX is:

Accepted Answer

A)  -6 - 4X -3/2. 
B)  -4X -3/2. 
C)  6 - 4X -3/2. 
D)  -6 - 4X -1/2. 
E)  -6 - X -3/2. 
A)  -6 - 4X -3/2. 
B)  -4X -3/2. 
C)  6 - 4X -3/2. 
D)  -6 - 4X -1/2. 
E)  -6 - X -3/2.

Question 14

You only have 12 ovens in which to bake over 200 specialty pastries.Subject to the oven constraint,you determine the profit-maximizing quantities of each pastry to produce and find that the Lagrangian multiplier is equal to 0.From this you conclude that you:

Accepted Answer

A)  should be producing fewer types of pastry. 
B)  should be producing more types of pastry. 
C)  should purchase additional ovens. 
D)  are effectively unconstrained with 12 ovens. 
E)  should purchase 2 more ovens. 
A)  should be producing fewer types of pastry. 
B)  should be producing more types of pastry. 
C)  should purchase additional ovens. 
D)  are effectively unconstrained with 12 ovens. 
E)  should purchase 2 more ovens.

Question 15

Whenever average profit is declining with increases in output,marginal

Accepted Answer

A)  revenue is less than marginal cost. 
B)  revenue is greater than marginal cost. 
C)  revenue is equal to marginal cost. 
D)  profit is less than average profit. 
E)  profit is negative. 
A)  revenue is less than marginal cost. 
B)  revenue is greater than marginal cost. 
C)  revenue is equal to marginal cost. 
D)  profit is less than average profit. 
E)  profit is negative.

Question 16

Marginal profit is maximized when:

Accepted Answer

A)  average profit is equal to marginal profit. 
B)  total profit is maximized. 
C)  average profit is increasing. 
D)  average profit is maximized. 
E)  average profit is decreasing. 
A)  average profit is equal to marginal profit. 
B)  total profit is maximized. 
C)  average profit is increasing. 
D)  average profit is maximized. 
E)  average profit is decreasing.

Question 17

If Y = aXb(c + Xd),then dY/dX is:

Accepted Answer

A)  abXb - 1(c + X)d + aXb dXd - 1. 
B)  abXb - 1(c + X)d + aXb(d - 1)Xd. 
C)  a(b - 1)Xb(c + Xd) + aXb(d - 1)Xd. 
D)  abXb - 1 dXd - 1. 
E)  a(b - 1)Xb(c + Xd). 
A)  abXb - 1(c + X)d + aXb dXd - 1. 
B)  abXb - 1(c + X)d + aXb(d - 1)Xd. 
C)  a(b - 1)Xb(c + Xd) + aXb(d - 1)Xd. 
D)  abXb - 1 dXd - 1. 
E)  a(b - 1)Xb(c + Xd).

Question 18

Total profit is maximized when:

Accepted Answer

A)  marginal profit equals average profit. 
B)  marginal profit equals zero. 
C)  average profit equals zero. 
D)  average profit is maximized. 
E)  marginal profit is greater than average profit. 
A)  marginal profit equals average profit. 
B)  marginal profit equals zero. 
C)  average profit equals zero. 
D)  average profit is maximized. 
E)  marginal profit is greater than average profit.

Question 19

The slope of a straight line is:

Accepted Answer

A)  positive. 
B)  negative. 
C)  zero. 
D)  constant. 
E)  nonconstant. 
A)  positive. 
B)  negative. 
C)  zero. 
D)  constant. 
E)  nonconstant.

Question 20

You must produce 200 records this week.Using the Lagrangian technique,you determine the profit-maximizing combination of pink vinyl and blue vinyl records and find that the Lagrangian multiplier is $2.50.From this you conclude that:

Accepted Answer

A)  the marginal revenue is about $2.50. 
B)  the average revenue is about $2.50. 
C)  the average revenue exceeds average cost by about $2.50. 
D)  the marginal revenue exceeds marginal cost by about $2.50. 
E)  consumers prefer pink vinyl to blue vinyl. 
A)  the marginal revenue is about $2.50. 
B)  the average revenue is about $2.50. 
C)  the average revenue exceeds average cost by about $2.50. 
D)  the marginal revenue exceeds marginal cost by about $2.50. 
E)  consumers prefer pink vinyl to blue vinyl.

A function of one argument is maximized when the first derivative:

Fox's Fine Furs (FFF)estimates that its total cost of production is TC = 125 + 100Q + 25Q².Furs sell for $1,100 each.To maximize profits,FFF should sell:

If Y = 3 / X,then d²Y/dX ² is:

Murdock Glass sells stained glass panes.Its profit is given by p = -500 + 100X - X².The profit-maximizing level of output is:

If Y = X³(5 + X ²)⁴,then dY/dX is:

Shag Express,a retailer of lamps,has determined that its total cost of retailing lamps is TC = 200 + 10Q + 5Q².At 10 units of output,the firm's marginal cost is:

NotAlligator Briefcases estimates that its total cost of producing vinyl bags is TC = 65 + 9 / Q + 5Q².At 3 units of output,NotAlligator's marginal cost is:

Campbell's sells used trailers,U,and new trailers,N.Its profits are given by p = 100N + 68U - 5N² - 5U² - 2NU.Campbell's maximum profit is:

If Y = -2 + X + 32X³,then dY/dX is:

If Y = U(X)W(X),then dY/dX is:

The second derivative of the total profit function is:

The first derivative of total profit with respect to quantity is:

If Y = 12 - 6X + 8X^-1/2,then dY/dX is:

You only have 12 ovens in which to bake over 200 specialty pastries.Subject to the oven constraint,you determine the profit-maximizing quantities of each pastry to produce and find that the Lagrangian multiplier is equal to 0.From this you conclude that you:

Whenever average profit is declining with increases in output,marginal

Marginal profit is maximized when:

If Y = aX^b(c + X^d),then dY/dX is:

Total profit is maximized when:

The slope of a straight line is:

You must produce 200 records this week.Using the Lagrangian technique,you determine the profit-maximizing combination of pink vinyl and blue vinyl records and find that the Lagrangian multiplier is $2.50.From this you conclude that:

Introduction

Demand Theory

Consumer Behavior and Rational Choice

Estimating Demand Functions

Production Theory

The Analysis of Costs

Perfect Competition

Monopoly and Monopolistic Competition

Managerial Use of Price Discrimination

Bundling and Intrafirm Pricing

Oligopoly

Game Theory

Auctions

Risk Analysis

Principalagent Issues and Managerial Compensation

Adverse Selection

Government and Business

Appendix Problems

Filters

Exam 18: Optimization Techniques

A function of one argument is maximized when the first derivative:

Fox's Fine Furs (FFF)estimates that its total cost of production is TC = 125 + 100Q + 25Q2.Furs sell for $1,100 each.To maximize profits,FFF should sell:

If Y = 3 / X,then d2Y/dX 2 is:

Murdock Glass sells stained glass panes.Its profit is given by p = -500 + 100X - X2.The profit-maximizing level of output is:

If Y = X3(5 + X 2)4,then dY/dX is:

Shag Express,a retailer of lamps,has determined that its total cost of retailing lamps is TC = 200 + 10Q + 5Q2.At 10 units of output,the firm's marginal cost is:

NotAlligator Briefcases estimates that its total cost of producing vinyl bags is TC = 65 + 9 / Q + 5Q2.At 3 units of output,NotAlligator's marginal cost is:

Campbell's sells used trailers,U,and new trailers,N.Its profits are given by p = 100N + 68U - 5N2 - 5U2 - 2NU.Campbell's maximum profit is:

If Y = -2 + X + 32X3,then dY/dX is:

If Y = U(X)W(X),then dY/dX is:

The second derivative of the total profit function is:

The first derivative of total profit with respect to quantity is:

If Y = 12 - 6X + 8X -1/2,then dY/dX is:

You only have 12 ovens in which to bake over 200 specialty pastries.Subject to the oven constraint,you determine the profit-maximizing quantities of each pastry to produce and find that the Lagrangian multiplier is equal to 0.From this you conclude that you:

Whenever average profit is declining with increases in output,marginal

Marginal profit is maximized when:

If Y = aXb(c + Xd),then dY/dX is:

Total profit is maximized when:

The slope of a straight line is:

You must produce 200 records this week.Using the Lagrangian technique,you determine the profit-maximizing combination of pink vinyl and blue vinyl records and find that the Lagrangian multiplier is $2.50.From this you conclude that:

Introduction

Demand Theory

Consumer Behavior and Rational Choice

Estimating Demand Functions

Production Theory

The Analysis of Costs

Perfect Competition

Monopoly and Monopolistic Competition

Managerial Use of Price Discrimination

Bundling and Intrafirm Pricing

Oligopoly

Game Theory

Auctions

Risk Analysis

Principalagent Issues and Managerial Compensation

Adverse Selection

Government and Business

Appendix Problems

Filters

Fox's Fine Furs (FFF)estimates that its total cost of production is TC = 125 + 100Q + 25Q².Furs sell for $1,100 each.To maximize profits,FFF should sell:

If Y = 3 / X,then d²Y/dX ² is:

Murdock Glass sells stained glass panes.Its profit is given by p = -500 + 100X - X².The profit-maximizing level of output is:

If Y = X³(5 + X ²)⁴,then dY/dX is:

Shag Express,a retailer of lamps,has determined that its total cost of retailing lamps is TC = 200 + 10Q + 5Q².At 10 units of output,the firm's marginal cost is:

NotAlligator Briefcases estimates that its total cost of producing vinyl bags is TC = 65 + 9 / Q + 5Q².At 3 units of output,NotAlligator's marginal cost is:

Campbell's sells used trailers,U,and new trailers,N.Its profits are given by p = 100N + 68U - 5N² - 5U² - 2NU.Campbell's maximum profit is:

If Y = -2 + X + 32X³,then dY/dX is:

If Y = 12 - 6X + 8X^-1/2,then dY/dX is:

If Y = aX^b(c + X^d),then dY/dX is: