exam Maths Puzzle Numerical Ability

A store wants to construct rectangular parking lot on land bordered on one side by a highway. It has 280 ft of fencing that is to be used to fence off the other three sides. What should be the dimensions of the lot if the enclosed area is to be a maximum?

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Derive the solution P(t)=MP0/P0+(M-P0)e power (-kMt) of the logistic initial value problem P'=kP(P-M), P(0)=P0. Make it clear how your derivation depends on wherher 0<P0<M or P0>M 3x+y=3