Solve Calculus Problem: Need Help!

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SUMMARY

The discussion revolves around solving a calculus optimization problem involving the area and cost of a rectangular plot. The equation for area is given as A = xy = 780, while the cost function is defined as cost = 8x + 2y. The user successfully derived the first derivative of the cost function, c' = 8 - (1560/x^2), and solved for x, obtaining x = 14. The corresponding value of y was determined to be 55, confirming that the optimal solution is option B.

PREREQUISITES
  • Understanding of calculus concepts, specifically optimization techniques.
  • Familiarity with derivatives and their applications in cost functions.
  • Knowledge of solving equations involving two variables.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Study optimization problems in calculus, focusing on real-world applications.
  • Learn about the method of Lagrange multipliers for constrained optimization.
  • Explore graphical methods for visualizing cost functions and constraints.
  • Practice solving similar calculus problems using different cost structures.
USEFUL FOR

Students studying calculus, particularly those focused on optimization problems, as well as educators looking for examples of real-world applications of calculus concepts.

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Calculus problem...please help!

Homework Statement



Here is a picture of the problem: http://i3.photobucket.com/albums/y62/Phio/23.jpg"

Homework Equations



A = xy = 780

cost = 8x+2y

The Attempt at a Solution



c = 8x + (1560/x)

c'= 8 - ( 1560/(x^2) )

0 = 8 - ( 1560/(x^2) )



x^2 = 195

x= \sqrt{195}

x = 13.96 = 14


I don't know what to do from here...I still can't figure out what the answer is. I think it must be either B or D.

Please help...thank you!
 
Last edited by a moderator:
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Find the corresponding value of y.
 


oh now I see it...it's obvious. The answer is B.

Thanks!
 

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