HOME WORK 2

Transportation Problem

QUESTION 1 Consider a problem of scheduling the weekly production of a particular item for the next 4 weeks. The production cost of the article is $ 10 for the first two weeks and $ 15 for the last two weeks. The weekly demands are 300, 700, 900, and 800, which must be met. The plan can produce a maximum of 700 units each week. In addition, the company can employ overtime during the second and third week. This increases the weekly production by an additional 200 units, but the production cost increases by $ 5 per item. Excess production can be stored at a unit cost of $ 3 per week. How should the production be scheduled to minimize the cost of production? Formulate the problem as a transportation model without backorder and solve it. EXPLAIN your answers clearly with detailed clarifications at every step.

QUESTION 2 Three electric power plants with capacities of 25, 40 and 30 million kWh supply electricity to three cities. The maximum demands at the three cities are estimated at 30, 35 and 25 million kWh. The price per million kWh at the three cities is given in the table below,

City

1 2 3 1 $600 $700 $400 PLANT 2 $320 $300 $350 3 $500 $480 $450 During the month of August, there is a 20% increase in demand in each of the three cities, which can be met by purchasing electricity from another network at a premium rate of $1000 per million kWh. The network is not linked to city 3, however. Therefore, the utility company wishes to determine the most economical plan for distributing and purchasing additional energy. a) Formulate the problem as a transportation model. b) Determine an optimal distribution plan for the utility company. c) Determine the cost of the additional power purchased by each of the cities.