Transportation$Assignmnet-Review Problems
Transportation$Assignmnet-Review Problems
Transportation$Assignmnet-Review Problems
My home has four valuable paintings that are up for sale. Four
customers are bidding for the paintings. Customer 1 is willing to buy two paintings,
but each other customer is willing to purchase at most one painting. The prices that
each customer is willing to pay for the paintings she is bidding are given in the table
below:
B
IN
T IN
IN
ID
T IN
T M
T M
T M
T M
- - - - -
- - - - -
- - - - -
IN
T IN
IN
- - - - - -
T IN
- - - - -
- - - - -
Determine how to maximize the total revenue received from the sale of the paintings.
First formulate a linear programming for the problem, then, solve it as linear
programming.
2.
50 tubes per week. Tubes are shipped to three customers. The profit earned per
tube depends on the site where the tubes were produced and on the customer who
purchases them (see the table below).
Customer 1 is willing to purchase up to 80 tubes per week; customer 2, up to 90;
and customer 3, up to 100.
(i)
Construct a balanced transportation problem that can be used to
maximize Televcos profits.
(ii)
Assume customer 3 is willing to buy any amount above his
original demand of 100 units for a discount price that will reduce the profit on
such a tube by 10%. Find the optimal plan for Tevelco using a balanced
transportation table.
(iii)
Extend part (ii) above to include customer 2 too. That is, assume
both customer 2 and customer 3 is willing to buy any amount above their
initial demand at a discount price which will reduce Televcos profit by 10%
per unit (for the additional amount). Modify the transportation table to
accommodate this change (do not forget to balance the table).
Plant 1
Plant 2
Plant 3
Customer 1
75
79
85
Customer 2
60
73
76
Customer 3
69
68
70
4. Oilco has oil fields in San Diego and Los Angeles. The San Diego field can
produce up to 500,000 barrels per day, and the Los Angeles field can produce up to
400,000 barrels per day. Oil is sent from the fields to a refinery, either in Dallas or in
Houston (assume that each refinery has unlimited capacity). It costs $700 to refine
100,000 barrels of oil at Dallas and $900 at Houston. Refined oil is shipped to
customers in Chicago and New York. Chicago customers require 400,000 barrels per
day of refined oil; New York customers require 300,000. The costs of shipping
100,000 barrels of oil (refined ore unrefined) between cities are given in the table
below. Create a balanced transportation table to model this situation. Solve as a linear
programming model.