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4.6 optimization #28a cylindrical container with no top is to be constructed to hold a fixed volume V0 of liquid. the cost of the material used for bottom is $0.50/in2 and cost of the material used for the curved lateral side is $0.30/in2 .use calculus to find radius (in terms of V0) of the leaset esxpensive container.

Question

4.6 optimization #28

a cylindrical container with no top is to be constructed to hold a fixed volume Vof liquid. the cost of the material used for bottom is $0.50/inand cost of the material used for the curved lateral side is $0.30/in.

use calculus to find radius (in terms of V0) of the leaset esxpensive container.

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Step 1

Consider that the radius of the cylindrical container with no top is r, and the height is h. The volume becomes V0 = πr2h. The area of the bottom is A1 = πr2 and the area of the curved lateral side is A2 = 2πrh. The material costs for the bottom and the curved lateral side are $0.50/in2 and $0.30/in2, respectively. The cost function for the total material used becomes

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Step 2

As V0 is fixed, h = V0/πr2, thus the modified cost function becomes  

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Step 3

Differentiate A with respe...

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