production planning

Question 1: (15 points) (This question can be answered in 20 minutes easily) We have to prepare an aggregate plan for the future 3 periods. Let the forecasted demands are D={250, 300, 330), unit production costs are p= {25, 30, 32}$, unit inventory holding costs are h={5, 5, 5}S, and production capacities are C = {500, 500, 600). Backlogging is not allowed. The system may increase its production capacity to 2 times of the given capacities by applying 2 shifts in a day. In a period, if the number of the shifts is 2 then we have 3000$ as a fixed cost of applying the second shift in addition to the given unit variable production costs. Fixed production set-up costs are A={6000, 6000, 6000). In a period, if there is a positive production then we have the fixed production set-up cost, otherwise we don't have it. Unit subcontracting cost is 60$. Develop the network flow problem type formulation of the