List of top Mathematics Questions on Optimization asked in PSEB XII

Divide a number 15 into two parts such that the square of one multiplied with the cube of the other is a maximum.
A wire of length 28m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and circle is minimized?