Explanation Given: Tabulate the given information. Crops Cost time Profit A $ 40 / acre 20 hours $ 150 / acre B $ 60 / acre 25 hours $ 200 / acre $ 200 / acre 3300 hours Approach: Let x is the number of acres to crop A and y is the number of acres to crop B . Then, the total profit P is P = 150 x + 200 y and this is the objective function to be maximized. The total amount of cost that is used by 40 x + 60 y minutes and must not exceed $ 7400 . So, the inequality is 40 x + 60 y ≤ 7400 . Similarly, the total amount of time that is used by 20 x + 25 y minutes and must not exceed $ 3300 . So, the inequality is 20 x + 25 y ≤ 3300 . Finally, neither x nor y will be negative, so, x ≥ 0 y ≥ 0 To summarize, the problem here is to maximize the objective function P = 150 x + 200 y subject to the system of inequalities. 40 x + 60 y ≤ 7400 20 x + 25 y ≤ 3300 x ≥ 0 , y ≥ 0 Figure(I) Conclusion: Hence, the units of each product that should be produced in each shift to maximize the company`s profit is given by P = 150 x + 200 y . Let c (in dollars) denote the contribution to the profit of a Product A . Then solve P = c x + 4 y solve for y , To determine b) The range of values that the resource associated with the constraint on the available land can assume. To determine c) The shadow price for the resource associated with the constraint on the available land.

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 3.4, Problem 12E

To determine

a)

The range of values that the contribution to the profit of an acre of Crop A can assume without changing the optimal solution.

To determine

b)

The range of values that the resource associated with the constraint on the available land can assume.

To determine

c)

The shadow price for the resource associated with the constraint on the available land.

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Chapter 3.4, Problem 11E

Chapter 3.4, Problem 13E

Chapter 3 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

Ch. 3.1 - Prob. 1CQ Ch. 3.1 - Prob. 2CQ Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - Prob. 6E Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - In Exercises 110, find the graphical solution to...

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a) The range of values that the contribution to the profit of an acre of Crop A can assume without changing the optimal solution.

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a) The range of values that the contribution to the profit of an acre of Crop A can assume without changing the optimal solution.

b) The range of values that the resource associated with the constraint on the available land can assume.

c) The shadow price for the resource associated with the constraint on the available land.

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Chapter 3 Solutions

a)

The range of values that the contribution to the profit of an acre of Crop A can assume without changing the optimal solution.

b)

The range of values that the resource associated with the constraint on the available land can assume.

c)

The shadow price for the resource associated with the constraint on the available land.