Tall-Brother company has three building projects in progress in this year. Each project needs a supply of bricks. There are three sources of bricks: red brick, black brick and grey brick available in the market, but shipping costs differ from location to location. The following Table summarizes the transportation costs.

Table 1

TO FROM Project 1 Project 2 Project 3 Tonnage allowance

Red brick station $9 $8 $7 3000

Black brick station $7 $11 $6 4000

Grey brick station $4 $3 $12 6000

Project requirements (tons) 2500 3750 4850

• Projects 1, 2 and 3 require 2500, 3750 and 4850 tons of brick supply respectively

• The red, black and grey brick stations have 3,000, 4,000 and 6,000 tons of bricks supply available respectively. The goal is to minimize the total transportation costs for the Tall-Brother company.

1) Formulate the corresponding LP problem and solve it using Excel to find the optimal transportation quantities so as to minimize the total transportation cost.

2) It is the case that Red brick station and Black brick station can send bricks by rail to Grey brick station for $1 per ton. Once the bricks are relocated. It can be trucked to the projects. Reformulate this problem and solve it via Excel to minimize the total transportation costs and corresponding optimal shipment quantities.