Homework #1: (Test yourself) The Garrett Company produces goods at its three plants and sells
them at its three retail outlets. After production, the goods are stored in the company’s two
warehouses until needed by the retail outlets. Trucks are used to transport the goods from the
plants to the warehouses, and ultimately from the warehouses to the retail outlets. The following
table shows the cost of shipping a unit from each plant to a warehouse.
Warehouse
Plant
P1
P2
P3
W1
425
510
450
W2
560
600
610
The daily production capacities of P1, P2, and P3 are 200, 200, and 100 units, respectively. The
next table shows the unit shipping cost from a warehouse to a retail outlet.
Warehouse
W1
W2
RO1
550
390
Retail Outlets
RO2
505
410
RO3
490
440
The daily demand at RO1, RO2, and RO3, are 130, 200, and 150 units, respectively.
(a) Create a linear program which determines the shipping schedule which meets demand and
minimizes the shipping cost.
(b) (Create a new copy of your spreadsheet in part (a).) Highway construction has blocked the
truck route from W1 to RO3. By changing the objective function (and not by adding or changing
a constraint), revise your model to determine the new minimum cost transportation schedule. In
this spreadsheet compute and label the change in costs due to the highway construction.
Homework#2: WellsCo is a fully integrated company that both produces goods and sells them at
its retail outlets. WellsCo produces product at two plants and stores the product at one of two
warehouses until shipment to one of WellsCo’s three retail outlets. Using units of full
truckloads, the table below shows each plant’s monthly output, its shipping cost per truckload
sent to each warehouse, and the maximum amount that it can ship per month to each warehouse.
From\To
Plant 1
Plant 2
Unit Shipping Cost
Warehouse1
Warehouse2
425
560
510
600
Shipping Capacity
Warehouse1 Warehouse2
125
150
175
200
Output
300
300
For each retail outlet (RO), the next table shows its monthly demand, its shipping cost per
truckload from each warehouse, and the maximum amount that can be shipped per month from
each warehouse.
From\To
Warehouse1
Warehouse2
Demand
Unit Shipping Cost
RO1
RO2
RO3
470
505
490
390
410
440
150
200
150
Shipping Capacity
RO1
RO2
RO3
100
150
100
125
150
75
You have been asked formulate and solve a linear program that will determine a distribution plan
(number of truckloads per month from each plant to each warehouse and from each warehouse to
each retail outlet) that will minimize the total shipping cost.