## The base and sides will cost $.01 per cm2 to produce but the top, which is plastic and resealable, will cost$.02 per cm2 to produce. What s

Question

The base and sides will cost $.01 per cm2 to produce but the top, which is plastic and resealable, will cost$.02 per cm2 to produce. What should the dimensions be to minimize cost?

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2 weeks 2021-09-13T21:23:19+00:00 1 Answer 0

1. Here is the full question

A snack food company wishes to have a cylinder package for it’s almond and cashew mix. The cylinder must contain 120 cm³ worth of product. The base and sides will cost $.01 per cm2 to produce but the top, which is plastic and resealable, will cost$.02 per cm2 to produce. What should the dimensions be to minimize cost?

The radius and height are both dimension in the cylinder; in order to minimize the cost

height = 18.93 cm

Step-by-step explanation:

We denote the radius of the cylinder to be = r

and the height of the cylinder = h

The volume of a cylinder is known to be = πr²h

Also, from the question; we are also told that the cylinder contains 120 πcm³

i.e πr²h = 120π

Dividing both sides with π; we have:

r²h = 120 The base and sides will cost $.01 per cm² to produce Total cost of the base and side = 0.01 ( πr² + 2πrh) but the top, which is plastic and resealable, will cost$.02 per cm² to produce.

i.e

cost of the top cylinder = 0.02 ( πr²)

Overall Total cost = = 0.01 ( πr² + 2πrh) + 0.02 ( πr²)

= 0.01 πr² + 0.02 πrh + 0.02 πr²

= = Taking the differentiation to find the radius dimension to minimize cost; we have:       cm

However,  Therefore; we can say that the cost is minimum at r = 2.515 since it is positive.

To determine the height ; we have:  h = 18.93 cm