Question: Solve the given maximum and minimum problems.

(JJ) A rectangular microprocessor chip is designed to have an area of \(25 \mathrm{~mm}^{2}\). What must be its dimensions if its perimeter is to be a minimum?

(KK) For the microprocessor chip mentioned in (JJ) above, show that the chip will always be a square for a given value of the area \(A\).

(LL) Ship a is travelling due east at \(18.0 \mathrm{~km} / \mathrm{h}\) as it passes a point \(40.0 \mathrm{~km}\) due south of ship b, which is travelling due south at \(16.0 \mathrm{~km} / \mathrm{h}\) how much later are the ships nearest each other?

(MM) A computer is programmed to display a slowly changing right triangle with its hypotenuse always equal to 12 cm. what are the legs of the triangle when it has its maximum area?

(NN) The printed area of a rectangular poster is \(384 \mathrm{~cm}^{2}\), win margins of \(4.00 \mathrm{~cm}\) on each side and margins of 6.00 cm the top and bottom. Find the dimensions of the poster with the smallest area.

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