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?

On solidification from a melt, the polymer polyethylene forms a semi-crystalline spherulite structure. (i) sketch an individual spherulite and label the amorphous and crystalline regions. (ii) draw a schematic to show the changes in specific volume with temperature during cooling from the melt, comparing it to the theoretical extremes of fully crystalline and fully amorphous (indicate tm and tg)