A) The top and bottom margins of a poster are 6 cm and the side margins are each

Question

A) The top and bottom margins of a poster are 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 390 square centimeters, find the dimensions of the poster with the smallest area.

Width =   ?            Height = ?

B) A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.

Total cost = ? (Round to the nearest penny and include monetary units. For example, if your answer is 1.095, enter $1.10 including the dollar sign and second decimal place.)

Explanation / Answer

Let x and y be the length and width of the poster (measured in cm).

Then the printed area is (x 8)(y 12) = 390.

So y = 12 + 390/( x 8 )

The area of the poster is S = xy = 12x + 384x /(x 8)

Solve S´ (x) = 0: 12 390 8/ (x 8)^2 = 0 x = 24.12

y=12+390/(24.12-8)=36.19

i can glad you help you but you should post the other exercise in another question thank you.

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