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3 (a). A company produces steel boxes at three different plants in amounts x, y and z respectively. Producing an annual revenue of F(x,y,z)=8xyz^2-200(x+y+z) . The company is to produce 100 units annually. How the production should be distributed to maximize revenue?

3 (a). A company produces steel boxes at three different plants in amounts x, y and z respectively. Producing an annual revenue of F(x,y,z)=8xyz^2-200(x+y+z) . The company is to produce 100 units annually. How the production should be distributed to maximize revenue?

Grade:12th pass

3 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
Dear student

Please write the Question in a standard form or attach an image of the question

Regards
Vikas TU
14149 Points
one year ago
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers
Arun
25763 Points
one year ago
Maximize  subject to . The Lagrangian is
 
with partial derivatives (set equal to 0):
 
 

From the first two equations it follows that . Subtracting either the first or second equation from the third tells us that
 
which means either , , or .
If , then , so that . So one critical point is (0, 0, 100).
If , then . So another critical point is (50, 50, 0).
If , then . So our third critical point is (25, 25, 50).
Evaluate the revenue function for each of these three critical points. You'll find that the latter critical point achieves the maximum value of 12,480,000 in revenue.
 

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