Labor fluctuating needs in construction projects can be met through hiring and end employment. Both activities incur cost. The goal is to minimize the total cost of acquiring needed labor force. A contractor estimates that the size of the workforce needed over the next 5 weeks is 5, 7, 8, 4, and 6 workers. Excess labor kept on the force will cost $300 per worker per week, and new hiring in any week will incur a fixed cost of $400 plus $200 per worker per week. Find the optimal solution for this problem through dynamic programming. How many workers require for each period and what is the minimum total cost