HOME WORK 2 Transportation Problem QUESTION 1 Consider a problem of scheduling the weekly production of a particular ite

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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.