Nanuq Europe has contracted to supply electric motors for commercial refrigerators which are produced by Nanuq International by April, 2012. The refrigerators are manufactured at four
locations: Jung (Sweden), Reynosa (Mexico), Pohang (South Korea) and East Tamaki (New Zealand). The electric motors are manufactured by Nanuq Europe which has three plants capable of producing these motors. These plants are located in Gaydon (UK), Rouen (France) and Dresden (Germany).
Nanuq Europe can produce 140,000 electric motors in Gaydon, 130,000 in Rouen and 160,000 in Dresden.
Nanuq International plans to produce 130,000 refrigerators in Jung, 120,000 in Reynosa, 145,000 in Pohang and 25,000 in East Tamaki.
Estimates of the costs (in Euros, €) of transportation per electric motor are summarised in the following table.
Supplied by Nanuq
Europe
to Nanuq International
Jung Reynosa Pohang East Tamaki
Gaydon 80 240 180 280
Rouen 40 210 200 320
Dresden 20 250 140 200
Nanuq Europe wants to determine how many electric motors should be transported from each plant to each destination minimising the cost of transporting.
(a) Determine the total demand for motors.
(b) Determine the total supply of motors.
(c) Construct a transportation tableau. (If required, introduce a dummy row or column.) Apply the Least Cost Method (the cheapest cell method).
(d) Interpret the starting solution from the least cost method.
(e) Obtain the optimal solution using Excel. Cut and paste the Excel output into Word document and interpret the solution.
(f) Calculate the total cost according to the Excel solution. Also comment on any excess supply or
demand.2
Problem 2
Four projects must be completed, and each of four employees will be assigned to work on exactly one of the four projects. The table below presents an estimate of the cost (that each employee would incur if working on the respective projects. Find the optimal solution using Excel.
PROJECT
EMPLOYEE 1 2 3 4
Mary $45,000 $32,000 $49,000 $55,000
Elizabeth $50,000 $45,000 $53,000 $43,000
Steven $52,000 $40,000 $70,000 $46,000
Joshua $60,000 $35,000 $40,000 $40,000