Question 1

If Y = 21X1/3(25 + X4),then dY/dX is:

Accepted Answer

A)  7X -2/3(25 + X4) + 84X10/3. 
B)  7X2/3(25 + X4) + 84X10/3. 
C)  7X -1/3(25 + X4) + 84X10/3. 
D)  7X1/3(25 + X4) + 84X10/3. 
E)  7X1/3(25 + X4). 
A)  7X -2/3(25 + X4) + 84X10/3. 
B)  7X2/3(25 + X4) + 84X10/3. 
C)  7X -1/3(25 + X4) + 84X10/3. 
D)  7X1/3(25 + X4) + 84X10/3. 
E)  7X1/3(25 + X4). A

Question 2

Gibbon's Restaurant finds that it sells more pizzas when it advertises according to S = 20 + 4A - 0.5A2,where S is sales and A is advertising expenditure.The sales-maximizing level of advertising is:

Accepted Answer

A)  A = $2. 
B)  A = $4. 
C)  A = $6. 
D)  A = $8. 
E)  A = $12. 
A)  A = $2. 
B)  A = $4. 
C)  A = $6. 
D)  A = $8. 
E)  A = $12. B

Question 3

If Y = 3X(X3),then d2Y/dX 2 is:

Accepted Answer

A)  6X 2. 
B)  12X3. 
C)  18X 2. 
D)  24X 2. 
E)  36X 2. 
A)  6X 2. 
B)  12X3. 
C)  18X 2. 
D)  24X 2. 
E)  36X 2. E

Question 4

The power rule of differentiation is:

Accepted Answer

A)  Y = aXb $\rarr$dY/dX = (b - 1)aXb - 1. 
B)  Y = aXb $\rarr$ dY/dX = (a - 1)bXa - 1. 
C)  Y = aXb $\rarr$dY/dX = (a - 1)aXa - 1. 
D)  Y = aXb $\rarr$dY/dX = (b - 1)bXb - 1. 
E)  Y = aXb $\rarr$dY/dX = baXb - 1. 
A)  Y = aXb $\rarr$dY/dX = (b - 1)aXb - 1. 
B)  Y = aXb $\rarr$ dY/dX = (a - 1)bXa - 1. 
C)  Y = aXb $\rarr$dY/dX = (a - 1)aXa - 1. 
D)  Y = aXb $\rarr$dY/dX = (b - 1)bXb - 1. 
E)  Y = aXb $\rarr$dY/dX = baXb - 1.

Question 5

If Y = (X - 3)2 / (9 + 12X - X4),then dY/dX is:

Accepted Answer

A)  [2(9 + 12X - X4)(X - 3) + (12 - 4X3)(X - 3)2] / (9 + 12X - X4)2. 
B)  [2(9 + 12X - X4)(X - 3) - (12 - 4X3)(X - 3)2] / (9 + 12X - X4)2. 
C)  [2(9 + 12X - X4)(X - 3) + (12 - 4X3)(X - 3)2](9 + 12X - X4)2. 
D)  [2(9 + 12X - X4)(X - 3) - (12 - 4X3)(X - 3)2](9 + 12X - X4)2. 
E)  [2(9 + 12X - X4)(X - 3) - (12 - 4X3)(X - 3)2] / (9 + 12X - X4). 
A)  [2(9 + 12X - X4)(X - 3) + (12 - 4X3)(X - 3)2] / (9 + 12X - X4)2. 
B)  [2(9 + 12X - X4)(X - 3) - (12 - 4X3)(X - 3)2] / (9 + 12X - X4)2. 
C)  [2(9 + 12X - X4)(X - 3) + (12 - 4X3)(X - 3)2](9 + 12X - X4)2. 
D)  [2(9 + 12X - X4)(X - 3) - (12 - 4X3)(X - 3)2](9 + 12X - X4)2. 
E)  [2(9 + 12X - X4)(X - 3) - (12 - 4X3)(X - 3)2] / (9 + 12X - X4).

Question 6

Whenever average profit is less than marginal profit:

Accepted Answer

A)  average profit declines with increases in output. 
B)  marginal profit decreases with increases in output. 
C)  marginal profit increases with increases in output. 
D)  average profit is maximized. 
E)  average profit increases with increases in output. 
A)  average profit declines with increases in output. 
B)  marginal profit decreases with increases in output. 
C)  marginal profit increases with increases in output. 
D)  average profit is maximized. 
E)  average profit increases with increases in output.

Question 7

Carmen's Detective Agency can use apprentice detectives,A,or experienced detectives,E.The cost of completing a job is C = 100 + A2 + E2 - 2AE.If a job requires a total of six detectives of either or both types,the cost-minimizing combination of detectives is:

Accepted Answer

A)  A = 3 and E = 3. 
B)  A = 2 and E = 4. 
C)  A = 4 and E = 2. 
D)  A = 6 and E = 0. 
E)  A = 0 and E = 6. 
A)  A = 3 and E = 3. 
B)  A = 2 and E = 4. 
C)  A = 4 and E = 2. 
D)  A = 6 and E = 0. 
E)  A = 0 and E = 6.

Question 8

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

Accepted Answer

A)  N = 9 and U = 5. 
B)  N = 7 and U = 7. 
C)  N = 5 and U = 9. 
D)  N = 13 and U = 0. 
E)  N = 9 and U = 9. 
A)  N = 9 and U = 5. 
B)  N = 7 and U = 7. 
C)  N = 5 and U = 9. 
D)  N = 13 and U = 0. 
E)  N = 9 and U = 9.

Question 9

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

Accepted Answer

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

Question 10

Too Much Fun (TMF)sells board games for the discerning student.It estimates that its total cost of sales is TC = Q + 27Q1/3.At 27 units of output,TMF's marginal cost is:

Accepted Answer

A)  $2. 
B)  $29. 
C)  $27. 
D)  $30. 
E)  $28. 
A)  $2. 
B)  $29. 
C)  $27. 
D)  $30. 
E)  $28.

Question 11

Slim's Shoe Repair has determined that its total cost of resoling shoes is TC = Q2 + 16Q1/2.At 16 units of output,Slim's marginal cost is:

Accepted Answer

A)  $324. 
B)  $64. 
C)  $256. 
D)  $34. 
E)  $2. 
A)  $324. 
B)  $64. 
C)  $256. 
D)  $34. 
E)  $2.

Question 12

If Y = (10 - X 2)1/2,then dY/dX is:

Accepted Answer

A)  -X(10 - X 2) -1/2. 
B)  1/2 (10 - X 2) -1/2. 
C)  -X(10 - X 2)1/2. 
D)  1/2(10 - X 2) -1/2. 
E)  none of the above. 
A)  -X(10 - X 2) -1/2. 
B)  1/2 (10 - X 2) -1/2. 
C)  -X(10 - X 2)1/2. 
D)  1/2(10 - X 2) -1/2. 
E)  none of the above.

Question 13

Al's Authentic Anklettes sells ankle bracelets.Their demand and costs are given by QD = 100 - P and TC = 100 + 10Q.The profit-maximizing level of output is:

Accepted Answer

A)  45 ankle bracelets. 
B)  47.5 ankle bracelets. 
C)  90 ankle bracelets. 
D)  10 ankle bracelets. 
E)  no ankle bracelets. 
A)  45 ankle bracelets. 
B)  47.5 ankle bracelets. 
C)  90 ankle bracelets. 
D)  10 ankle bracelets. 
E)  no ankle bracelets.

Question 14

The constant rule of differentiation is:

Accepted Answer

A)  Y = a + bX $\rarr$ dY/dX = a + b 
B)  Y = a + bX $\rarr$ dY/dX = a 
C)  Y = a + bX$\rarr$dY/dX = b 
D)  Y = a + bX $\rarr$dY/dX = ab 
E)  Y = a + bX$\rarr$ dY/dX = ab 
A)  Y = a + bX $\rarr$ dY/dX = a + b 
B)  Y = a + bX $\rarr$ dY/dX = a 
C)  Y = a + bX$\rarr$dY/dX = b 
D)  Y = a + bX $\rarr$dY/dX = ab 
E)  Y = a + bX$\rarr$ dY/dX = ab

Question 15

The chain rule of differentiation is:

Accepted Answer

A)  Y = U(W(X)) $\rarr$dY/dX = dY/dX dW/dX. 
B)  Y = U(W(X))$\rarr$ dY/dX = dU/dW dW/dX. 
C)  Y = U(W(X))$\rarr$ dY/dX = dU/dX dW/dX. 
D)  Y = U(W(X)) $\rarr$ dY/dX = dW/dU dU/dX. 
E)  Y = U(W(X)) $\rarr$ dY/dX = dU/dU dU/dX. 
A)  Y = U(W(X)) $\rarr$dY/dX = dY/dX dW/dX. 
B)  Y = U(W(X))$\rarr$ dY/dX = dU/dW dW/dX. 
C)  Y = U(W(X))$\rarr$ dY/dX = dU/dX dW/dX. 
D)  Y = U(W(X)) $\rarr$ dY/dX = dW/dU dU/dX. 
E)  Y = U(W(X)) $\rarr$ dY/dX = dU/dU dU/dX.

Question 16

If Y = 3X / (3X + X 2),then dY/dX is:

Accepted Answer

A)  [(3 + 2X)3X + 3(3X + X 2)] / (3X + X 2)2. 
B)  (3 + 2X)3X / (3X + X2)2. 
C)  -3 / (3 + X)2. 
D)  [(3 + 2X) - 3(3X + X 2)] / (3X + X 2)2. 
E)  (3 + 2X)3X / (3X + X2). 
A)  [(3 + 2X)3X + 3(3X + X 2)] / (3X + X 2)2. 
B)  (3 + 2X)3X / (3X + X2)2. 
C)  -3 / (3 + X)2. 
D)  [(3 + 2X) - 3(3X + X 2)] / (3X + X 2)2. 
E)  (3 + 2X)3X / (3X + X2).

Question 17

Wilma's Car Repair can repair cars using kryptonite bolts,K,or lithium bolts,L,as long as it uses 10 bolts in toto.The cost of repairing a car is TC = K2 + L2 - KL.The cost-minimizing combination of kryptonite and lithium bolts is:

Accepted Answer

A)  K = 6 and L = 4. 
B)  K = 4 and L = 6. 
C)  K = 7 and L = 3. 
D)  K = 3 and L = 7. 
E)  K = 5 and L = 5. 
A)  K = 6 and L = 4. 
B)  K = 4 and L = 6. 
C)  K = 7 and L = 3. 
D)  K = 3 and L = 7. 
E)  K = 5 and L = 5.

Question 18

The product rule of differentiation is:

Accepted Answer

A)  Y = U(X)W(X) $\rarr$dY/dX = (U dW/dX)(W dU/dX). 
B)  Y = U(X)W(X) $\rarr$dY/dX = (W dW/dX) / (U dU/dX). 
C)  Y = U(X)W(X) $\rarr$ dY/dX = (U dW/dX) - (W dU/dX). 
D)  Y = U(X)W(X) $\rarr$ dY/dX = (U dW/dX) + (W dU/dX). 
E)  Y = U(X)W(X) $\rarr$ dY/dX = (W dW/dX) + (U dU/dX). 
A)  Y = U(X)W(X) $\rarr$dY/dX = (U dW/dX)(W dU/dX). 
B)  Y = U(X)W(X) $\rarr$dY/dX = (W dW/dX) / (U dU/dX). 
C)  Y = U(X)W(X) $\rarr$ dY/dX = (U dW/dX) - (W dU/dX). 
D)  Y = U(X)W(X) $\rarr$ dY/dX = (U dW/dX) + (W dU/dX). 
E)  Y = U(X)W(X) $\rarr$ dY/dX = (W dW/dX) + (U dU/dX).

Question 19

When using the Lagrangian technique for solving a constrained cost-minimization problem,the Lagrangian multiplier $\lambda$ is:

Accepted Answer

A)  the optimal level of cost. 
B)  the minimized marginal cost. 
C)  the minimized total cost. 
D)  the maximized profit. 
E)  equal to zero. 
A)  the optimal level of cost. 
B)  the minimized marginal cost. 
C)  the minimized total cost. 
D)  the maximized profit. 
E)  equal to zero.

Question 20

Instructed to choose the combination of inputs that minimizes the cost of producing 2,000 pan-head screws,your assistant returns with the startling news that the Lagrangian multiplier is $0.10.From this you conclude that:

Accepted Answer

A)  costs have not been minimized. 
B)  the average cost of producing screws at 2,000 units is $0.10. 
C)  the marginal cost of producing screws at 2,000 units is $0.10. 
D)  marginal cost equals average cost. 
E)  the price of the screws must be $0.10. 
A)  costs have not been minimized. 
B)  the average cost of producing screws at 2,000 units is $0.10. 
C)  the marginal cost of producing screws at 2,000 units is $0.10. 
D)  marginal cost equals average cost. 
E)  the price of the screws must be $0.10.

If Y = 21X^1/3(25 + X⁴),then dY/dX is:

Gibbon's Restaurant finds that it sells more pizzas when it advertises according to S = 20 + 4A - 0.5A²,where S is sales and A is advertising expenditure.The sales-maximizing level of advertising is:

If Y = 3X(X³),then d²Y/dX ² is:

The power rule of differentiation is:

If Y = (X - 3)² / (9 + 12X - X⁴),then dY/dX is:

Whenever average profit is less than marginal profit:

Carmen's Detective Agency can use apprentice detectives,A,or experienced detectives,E.The cost of completing a job is C = 100 + A² + E² - 2AE.If a job requires a total of six detectives of either or both types,the cost-minimizing combination of detectives is:

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

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

Too Much Fun (TMF)sells board games for the discerning student.It estimates that its total cost of sales is TC = Q + 27Q^1/3.At 27 units of output,TMF's marginal cost is:

Slim's Shoe Repair has determined that its total cost of resoling shoes is TC = Q² + 16Q^1/2.At 16 units of output,Slim's marginal cost is:

If Y = (10 - X ²)^1/2,then dY/dX is:

Al's Authentic Anklettes sells ankle bracelets.Their demand and costs are given by Q^D = 100 - P and TC = 100 + 10Q.The profit-maximizing level of output is:

The constant rule of differentiation is:

The chain rule of differentiation is:

If Y = 3X / (3X + X ²),then dY/dX is:

Wilma's Car Repair can repair cars using kryptonite bolts,K,or lithium bolts,L,as long as it uses 10 bolts in toto.The cost of repairing a car is TC = K² + L² - KL.The cost-minimizing combination of kryptonite and lithium bolts is:

The product rule of differentiation is:

When using the Lagrangian technique for solving a constrained cost-minimization problem,the Lagrangian multiplier $\lambda$ is:

Instructed to choose the combination of inputs that minimizes the cost of producing 2,000 pan-head screws,your assistant returns with the startling news that the Lagrangian multiplier is $0.10.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

If Y = 21X1/3(25 + X4),then dY/dX is:

Gibbon's Restaurant finds that it sells more pizzas when it advertises according to S = 20 + 4A - 0.5A2,where S is sales and A is advertising expenditure.The sales-maximizing level of advertising is:

If Y = 3X(X3),then d2Y/dX 2 is:

The power rule of differentiation is:

If Y = (X - 3)2 / (9 + 12X - X4),then dY/dX is:

Whenever average profit is less than marginal profit:

Carmen's Detective Agency can use apprentice detectives,A,or experienced detectives,E.The cost of completing a job is C = 100 + A2 + E2 - 2AE.If a job requires a total of six detectives of either or both types,the cost-minimizing combination of detectives is:

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

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

Too Much Fun (TMF)sells board games for the discerning student.It estimates that its total cost of sales is TC = Q + 27Q1/3.At 27 units of output,TMF's marginal cost is:

Slim's Shoe Repair has determined that its total cost of resoling shoes is TC = Q2 + 16Q1/2.At 16 units of output,Slim's marginal cost is:

If Y = (10 - X 2)1/2,then dY/dX is:

Al's Authentic Anklettes sells ankle bracelets.Their demand and costs are given by QD = 100 - P and TC = 100 + 10Q.The profit-maximizing level of output is:

The constant rule of differentiation is:

The chain rule of differentiation is:

If Y = 3X / (3X + X 2),then dY/dX is:

Wilma's Car Repair can repair cars using kryptonite bolts,K,or lithium bolts,L,as long as it uses 10 bolts in toto.The cost of repairing a car is TC = K2 + L2 - KL.The cost-minimizing combination of kryptonite and lithium bolts is:

The product rule of differentiation is:

When using the Lagrangian technique for solving a constrained cost-minimization problem,the Lagrangian multiplier λ\lambdaλ is:

Instructed to choose the combination of inputs that minimizes the cost of producing 2,000 pan-head screws,your assistant returns with the startling news that the Lagrangian multiplier is $0.10.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

If Y = 21X^1/3(25 + X⁴),then dY/dX is:

Gibbon's Restaurant finds that it sells more pizzas when it advertises according to S = 20 + 4A - 0.5A²,where S is sales and A is advertising expenditure.The sales-maximizing level of advertising is:

If Y = 3X(X³),then d²Y/dX ² is:

If Y = (X - 3)² / (9 + 12X - X⁴),then dY/dX is:

Carmen's Detective Agency can use apprentice detectives,A,or experienced detectives,E.The cost of completing a job is C = 100 + A² + E² - 2AE.If a job requires a total of six detectives of either or both types,the cost-minimizing combination of detectives is:

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

Too Much Fun (TMF)sells board games for the discerning student.It estimates that its total cost of sales is TC = Q + 27Q^1/3.At 27 units of output,TMF's marginal cost is:

Slim's Shoe Repair has determined that its total cost of resoling shoes is TC = Q² + 16Q^1/2.At 16 units of output,Slim's marginal cost is:

If Y = (10 - X ²)^1/2,then dY/dX is:

Al's Authentic Anklettes sells ankle bracelets.Their demand and costs are given by Q^D = 100 - P and TC = 100 + 10Q.The profit-maximizing level of output is:

If Y = 3X / (3X + X ²),then dY/dX is:

Wilma's Car Repair can repair cars using kryptonite bolts,K,or lithium bolts,L,as long as it uses 10 bolts in toto.The cost of repairing a car is TC = K² + L² - KL.The cost-minimizing combination of kryptonite and lithium bolts is:

When using the Lagrangian technique for solving a constrained cost-minimization problem,the Lagrangian multiplier $\lambda$ is: