Chapter 7.1, Problem 2P

A contractor owns three excavators of different capacity. He/she wants to dispatch these excavatorsinto three different jobs. The performance of the excavators is measured as the time consumed toperform each job. The data of the time tests are shown as given in the table below. (a) Draw a network flow diagram.(b) Formulate a mathematical model to obtain the minimum time.(c) Solve this model using the Vogel’s approximation model.

Vandelay Industries has 275 sales reps in order to sell its latex products, each to be assigned to one of four marketing teams. If the first team is to have four times as many members as the second team and the third team is to have five times as many members as the fourth team, how can the members be distributed among the teams?

Consider a sequence of operations fi= 1,2,3, ⋯ , m. Use the Potential method. First, define the amortized cost ai and the actual cost ti for each operation fi. Hint: you need to first define the potential function and find the relationship between amortized cost, true cost, and the change in potential. Then, show that the amortized cost of the entire sequence of operations is at least the total actual cost. Full marks are given for complete mathematical formulation.