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Alex787 [66]
3 years ago
6

Optimization. A rectangle is to have an area of 32 square cms. Find its dimensions so that

Mathematics
1 answer:
arsen [322]3 years ago
6 0
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

xy = 32 makes y = 32/x z² = (32/x)² + (x/2)²

<span>Isolate z
</span>z = 32/x + x/2 

Find dz/dx

fr(z) = (x² - 64)/ (2x²)

<span>Set z' = 0, algebraically solving for x having
</span>x +- 18

<span>Since you cannot have a dimension of -8, the only answer for x is 8.
</span>
<span>Go back to the original area equation; 32 = xy and plug in x making
</span><span>32 = 8y
</span><span>y = 4</span>
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