Design a dynamic programming algorithm for the following problem. find the maximum total sale price that can be obtained by cutting a rod of n units long into integer-length pieces if the sale price of a piece i units long is pi for i = 1, 2, . . , n. what are the time and space efficiencies of your algorithm?

An electrical kettle is made out of stainless steel,weighs two pounds (when empty) with a heating element that consumes 2 kw of electricity. assuming that the water and the kettle are at the same uniform temperature at any moment of time, calculate the shortest possible time to bring 2 quarts of water from room temperature to the onset of boiling.