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Grade: 12th pass

                        

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 years ago

Answers : (3)

Saurabh Koranglekar
askIITians Faculty
8407 Points
							Dear student

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

Regards
6 months ago
Vikas TU
12281 Points
							
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers
6 months ago
Arun
24735 Points
							
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.
 
6 months ago
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