Explanation Given: The maximum number of animals raised at a time is 16. The maximum number of goats raised at a time is 10. The cost to raise one goat is $25, and the cost to raise one pig is $75. The maximum cost available to raise the animals is $900. The profit gained from one goat is $12, and the cost to raise one pig is $40. Explanation: The constraints as provided by the original problem are x + y ≤ 16 25 x + 75 y ≤ 900 x ≤ 10 x ≥ 0 y ≥ 0 The original objective function is z = 12 x + 40 y The graph of the linear inequalities as provided by the original solution is The optimal solution of the original problem is at the corner point ( 0 , 12 ) . Let the cost to raise one goat decrease from $25to $ ( 25 − b ) . The cost constraint inequality can be written as ( 25 − b ) x + 75 y ≤ 900 The corresponding boundary line is ( 25 − b ) x + 75 y = 900 y = − ( 25 − b ) 75 + 12 The slope of this boundary line is − ( 25 − b ) 75 . The cost change to raise one goat also reflects on the profit from one goat raised. The new objective function is z = ( 12 + b ) x + 40 y y = − ( 12 + b ) 40 x + z 40 The slope of the isoprofit lines for this objective function is − ( 12 + b ) 40

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency o…

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

Videos

Question

Chapter 3, Problem 3EA

To determine

The smallest decrease in the cost of one goat raised such that the optimal solution of 0 goats and 12 pigs raised changes.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 2EA

Chapter 3, Problem 4EA

Students have asked these similar questions

Solve this questions please

Find all positive integers n such that n.2n +1 is a square.

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who support labeling legislation for genetically modified organisms (GMOs). Her estimate must be accurate within 4% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 65% of the respondents said they support labeling legislation for GMOs. (c) Compare the results from parts (a) and (b). ... (a) What is the minimum sample size needed assuming that no prior information is available? n = (Round up to the nearest whole number as needed.)

Chapter 3 Solutions

Finite Mathematics (11th Edition)

Ch. 3.1 - Graph each linear inequality. x + y 2 Ch. 3.1 - Graph each linear inequality. y x + 1 Ch. 3.1 - Graph each linear inequality. x 2 y Ch. 3.1 - Graph each linear inequality. y x 3 Ch. 3.1 - Graph each linear inequality. 4x y 6 Ch. 3.1 - Graph each linear inequality. 4y + x 6 Ch. 3.1 - Graph each linear inequality. 7. 4x + y 8 Ch. 3.1 - Graph each linear inequality. 2x y 2 Ch. 3.1 - Graph each linear inequality. x + 3y 2 Ch. 3.1 - Graph each linear inequality. 2x + 3y 6

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The smallest decrease in the cost of one goat raised such that the optimal solution of 0 goats and 12 pigs raised changes.

Solution Summary: The author determines the optimal solution of 0 goats and 12 pigs raised. The cost of one goat raised must decrease by at least 0.87.

Concept explainers

Videos

The smallest decrease in the cost of one goat raised such that the optimal solution of 0 goats and 12 pigs raised changes.

Want to see the full answer?

Chapter 3 Solutions