(a) To plot: The graph of the profit as a function of the number of widgets manufactured in a week.

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Answer 1

Question

Chapter 6.3, Problem 12E

To determine

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

To determine

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

To determine

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

To determine

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

To determine

(e)

The marginal profit at the production level found in part (d).

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Let 2 A = 4 3 -4 0 1 (a) Show that v = eigenvalue. () is an eigenvector of A and find the corresponding (b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a) may be useful. (c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.

(c) Let 6 0 0 A = -10 4 8 5 1 2 (i) Find the characteristic polynomial of A and factorise it. (ii) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (iii) Is A diagonalisable? Give reasons for your answer.

most 2, and let Let P2 denote the vector space of polynomials of degree at D: P2➡ P2 be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative p'(t) 2at+b, that is, D(p) = p'. (a) Prove that D is a linear transformation. (b) Find a basis for the kernel ker(D) of the linear transformation D and compute its nullity. (c) Find a basis for the image im(D) of the linear transformation D and compute its rank. (d) Verify that the Rank-Nullity Theorem holds for the linear transformation D. (e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.

Answer 2

Question

Chapter 6.3, Problem 12E

To determine

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

To determine

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

To determine

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

To determine

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

To determine

(e)

The marginal profit at the production level found in part (d).

Expert Solution & Answer

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Answer 3

Question

Chapter 6.3, Problem 12E

To determine

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

To determine

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

To determine

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

To determine

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

To determine

(e)

The marginal profit at the production level found in part (d).

Expert Solution & Answer

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Answer 4

Question

Chapter 6.3, Problem 12E

To determine

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

To determine

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

To determine

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

To determine

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

To determine

(e)

The marginal profit at the production level found in part (d).

Expert Solution & Answer

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Answer 5

Chapter 6.3, Problem 12E

To determine

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

To determine

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

To determine

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

To determine

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

To determine

(e)

The marginal profit at the production level found in part (d).

Answer 6

Chapter 6.3, Problem 12E

To determine

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

Answer 7

Chapter 6.3, Problem 12E

To determine

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

Answer 8

To determine

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

Answer 9

To determine

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

Answer 10

To determine

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

Answer 11

To determine

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

Answer 12

To determine

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

Answer 13

To determine

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

Answer 14

To determine

(e)

The marginal profit at the production level found in part (d).

Answer 15

To determine

(e)

The marginal profit at the production level found in part (d).

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

(a) To plot: The graph of the profit as a function of the number of widgets manufactured in a week.

Solution Summary: The author explains how to plot the profit as a function of the number of widgets manufactured in the week.

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

(e)

The marginal profit at the production level found in part (d).

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Chapter 6 Solutions

(a) To plot: The graph of the profit as a function of the number of widgets manufactured in a week.

Solution Summary: The author explains how to plot the profit as a function of the number of widgets manufactured in the week.

(a) To plot: The graph of the profit as a function of the number of widgets manufactured in a week.

(b) The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

(c) The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

(d) To find: Number of widgets to be produced in a week to maximize profit.

(e) The marginal profit at the production level found in part (d).

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Chapter 6 Solutions

(a)

To plot:

The graph of the profit as a function of the number of widgets manufactured in a week.

(b)

The marginal profit if the firm produces 10 widgets in a week, and meaning in practical terms.

(c)

The marginal profit if the firm produces 15 widgets in a week and meaning in practical terms.

(d)

To find:

Number of widgets to be produced in a week to maximize profit.

(e)

The marginal profit at the production level found in part (d).