Question

You are designing the top of a pencil pouch that consists of a rectangle to which...

You are designing the top of a pencil pouch that consists of a rectangle to which a semi circle has been attached to both ends (see the sketch). The semicircles will be made from a material that costs 1ct per square centimeter. The material of the rectangular part costs 4ct per square centimeter. The perimeter of the pouch must be 80cm. How do you have to choose the radius and the ‘open’ side of the rectangle so that the cost is minimal? Before you start, label your sketch!

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Answer #1

vert let radius of semi circle be Aim and length of rectangle of be acme den - Breadth will become = 24 cm Give, perimeter ahale get C = Th² + or TT so- TH?+ 3301 - 80 1 = 3dor - 7tr² for minimum cst put clr) = 0 330 - 14 = 3d0 - 14(34Azo | 320 - 4

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