Explanation Given: A profit function representing the profit gain. P ( x , y ) = 3 x 2 + 4 y 2 − 4 x y Where x represents the number of units sold of tranquilizer and y represents the number of units sold of antibiotic. In first condition the y remains constant while the sale of x is increased from 9 to 10. In second case the x remains constant and value of y is increased from 5 to 6. Calculation: (a) Consider the profit function and calculate the first partial derivative of the function. Consider as in first case that x is increased and y remains constant. Hence, take partial derivative with respect to x as mentioned below. P x = ∂ ∂ x ( 3 x 2 + 4 y 2 − 4 x y ) = 6 x − 4 y Further, determine the value of P x ( 9 , 5 ) to calculate profit margin in case the sales of tranquilizer is increased from 9 to 10

12th Edition

ISBN: 8220106844557

Author: MULLINS

Publisher: PEARSON

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Chapter 14.2, Problem 45E

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To calculate:

(a) Value of Px(9,5), the approximate effect on profit if the tranquilizer’s sales is increased from 9 to 10 units.

(b) Value of Py(9,5), the approximate effect on profit if the sales of antibiotic is increased from 5 to 6 units.

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Chapter 14.2, Problem 44E

Chapter 14.2, Problem 43E

Chapter 14 Solutions

EBK MATHEMATICS WITH APPLICATIONS IN TH

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Checkout Lines According to...Ch. 14.1 - Prob. 40E Ch. 14.1 - Prob. 41E Ch. 14.1 - Prob. 42E Ch. 14.1 - Prob. 43E Ch. 14.1 - Prob. 44E Ch. 14.1 - Prob. 45E Ch. 14.1 - Prob. 46E Ch. 14.1 - Prob. 47E Ch. 14.1 - Prob. 48E Ch. 14.2 - Prob. 1CP Ch. 14.2 - Prob. 2CP Ch. 14.2 - Prob. 3CP Ch. 14.2 - Prob. 4CP Ch. 14.2 - Prob. 5CP Ch. 14.2 - Prob. 6CP Ch. 14.2 - Prob. 7CP Ch. 14.2 - Prob. 8CP Ch. 14.2 - Prob. 9CP Ch. 14.2 - Prob. 1E Ch. 14.2 - For each of the given functions, find the...Ch. 14.2 - Prob. 3E Ch. 14.2 - Prob. 4E Ch. 14.2 - Prob. 5E Ch. 14.2 - Prob. 6E Ch. 14.2 - Prob. 7E Ch. 14.2 - Prob. 8E Ch. 14.2 - Prob. 9E Ch. 14.2 - Prob. 10E Ch. 14.2 - Prob. 11E Ch. 14.2 - Prob. 12E Ch. 14.2 - Prob. 13E Ch. 14.2 - Prob. 14E Ch. 14.2 - Prob. 15E Ch. 14.2 - Prob. 16E Ch. 14.2 - Prob. 17E Ch. 14.2 - Prob. 18E Ch. 14.2 - Prob. 19E Ch. 14.2 - Prob. 20E Ch. 14.2 - Prob. 21E Ch. 14.2 - Prob. 22E Ch. 14.2 - Prob. 23E Ch. 14.2 - Prob. 24E Ch. 14.2 - Prob. 25E Ch. 14.2 - Prob. 26E Ch. 14.2 - Prob. 27E Ch. 14.2 - Prob. 28E Ch. 14.2 - Prob. 29E Ch. 14.2 - Prob. 30E Ch. 14.2 - Prob. 31E Ch. 14.2 - Prob. 32E Ch. 14.2 - Prob. 33E Ch. 14.2 - Prob. 34E Ch. 14.2 - Prob. 35E Ch. 14.2 - Prob. 36E Ch. 14.2 - Prob. 37E Ch. 14.2 - Find fx,fy,fz, and fyz for the given functions. In...Ch. 14.2 - Prob. 39E Ch. 14.2 - Suppose z=f(x,y) describes the cost to build a...Ch. 14.2 - Prob. 41E Ch. 14.2 - 42. Business The revenue from the sale of x units...Ch. 14.2 - Prob. 62E Ch. 14.2 - Prob. 44E Ch. 14.2 - Prob. 45E Ch. 14.2 - Prob. 43E Ch. 14.2 - Prob. 42E Ch. 14.2 - Prob. 59E Ch. 14.2 - Prob. 50E Ch. 14.2 - Prob. 51E Ch. 14.2 - Work the following applied problems. (See Example...Ch. 14.2 - Prob. 53E Ch. 14.2 - Work the following marginal productivity problems....Ch. 14.2 - Prob. 55E Ch. 14.2 - Prob. 56E Ch. 14.2 - Prob. 58E Ch. 14.2 - Work the following applied problems. 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Explain the difference between the two methods...Ch. 14.4 - Prob. 19E Ch. 14.4 - Prob. 20E Ch. 14.4 - Prob. 21E Ch. 14.4 - Prob. 22E Ch. 14.4 - Prob. 23E Ch. 14.4 - Prob. 24E Ch. 14.4 - Prob. 25E Ch. 14.4 - Prob. 26E Ch. 14.4 - Prob. 27E Ch. 14.4 - Prob. 28E Ch. 14.4 - Prob. 29E Ch. 14.4 - Prob. 30E Ch. 14.4 - Prob. 31E Ch. 14.4 - Prob. 32E Ch. 14.4 - Prob. 33E Ch. 14.4 - Prob. 34E Ch. 14.4 - Prob. 35E Ch. 14.4 - Prob. 36E Ch. 14 - Prob. 1RE Ch. 14 - Prob. 2RE Ch. 14 - Prob. 3RE Ch. 14 - Prob. 4RE Ch. 14 - Prob. 5RE Ch. 14 - Prob. 6RE Ch. 14 - Prob. 7RE Ch. 14 - Prob. 8RE Ch. 14 - Prob. 9RE Ch. 14 - Prob. 10RE Ch. 14 - Prob. 11RE Ch. 14 - Prob. 12RE Ch. 14 - Prob. 13RE Ch. 14 - Prob. 14RE Ch. 14 - Prob. 15RE Ch. 14 - Prob. 16RE Ch. 14 - Prob. 17RE Ch. 14 - Prob. 18RE Ch. 14 - Prob. 19RE Ch. 14 - Prob. 20RE Ch. 14 - Prob. 21RE Ch. 14 - Prob. 22RE Ch. 14 - Prob. 23RE Ch. 14 - Prob. 24RE Ch. 14 - Prob. 25RE Ch. 14 - Prob. 26RE Ch. 14 - Prob. 27RE Ch. 14 - Prob. 28RE Ch. 14 - Prob. 29RE Ch. 14 - Prob. 30RE Ch. 14 - Prob. 31RE Ch. 14 - Prob. 32RE Ch. 14 - Prob. 33RE Ch. 14 - Prob. 34RE Ch. 14 - Prob. 35RE Ch. 14 - Prob. 36RE Ch. 14 - Prob. 37RE Ch. 14 - Prob. 38RE Ch. 14 - Prob. 39RE Ch. 14 - Prob. 40RE Ch. 14 - Prob. 41RE Ch. 14 - Prob. 42RE Ch. 14 - Prob. 43RE Ch. 14 - Prob. 44RE Ch. 14 - Prob. 45RE Ch. 14 - Prob. 46RE Ch. 14 - Prob. 47RE Ch. 14 - Prob. 48RE Ch. 14 - Prob. 49RE Ch. 14 - Prob. 50RE Ch. 14 - 51. 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(a) Value of P x ( 9 , 5 ) , the approximate effect on profit if the tranquilizer’s sales is increased from 9 to 10 units. (b) Value of P y ( 9 , 5 ) , the approximate effect on profit if the sales of antibiotic is increased from 5 to 6 units.

Solution Summary: The author calculates the profit margin by calculating the value of P_x(9,5), where x represents the number of units sold of tranquilizer.

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To calculate:

(a) Value of Px(9,5), the approximate effect on profit if the tranquilizer’s sales is increased from 9 to 10 units.

(b) Value of Py(9,5), the approximate effect on profit if the sales of antibiotic is increased from 5 to 6 units.

Want to see the full answer?

Chapter 14 Solutions

(a) Value of P x ( 9 , 5 ) , the approximate effect on profit if the tranquilizer’s sales is increased from 9 to 10 units. (b) Value of P y ( 9 , 5 ) , the approximate effect on profit if the sales of antibiotic is increased from 5 to 6 units.

Solution Summary: The author calculates the profit margin by calculating the value of P_x(9,5), where x represents the number of units sold of tranquilizer.

Videos

To calculate: (a) Value of Px(9,5), the approximate effect on profit if the tranquilizer’s sales is increased from 9 to 10 units. (b) Value of Py(9,5), the approximate effect on profit if the sales of antibiotic is increased from 5 to 6 units.

Want to see the full answer?

Chapter 14 Solutions

To calculate:

(a) Value of Px(9,5), the approximate effect on profit if the tranquilizer’s sales is increased from 9 to 10 units.

(b) Value of Py(9,5), the approximate effect on profit if the sales of antibiotic is increased from 5 to 6 units.