1. A producer of pleasure boats wants to maximize revenue during the next season. Two types of boats are sold i.e. speedboat (X1) and pontoon (X2). The speedboat sells for $40,000 and the pontoon sells for $30,000. The speedboat takes 10 weeks to manufacture and the pontoon takes 3 weeks. One speedboat uses 600 meters of board and the pontoon uses 1000 meters of board. Each speedboat requires 500 square meters of fiberglass, while each pontoon requires 200 square meters of fiberglass. There are 30 weeks of labor, 3,600 meters of board, and 1,800 square meters of fiberglass available. Due to space constraints not more than 3 pontoons and not more than 4 speedboats can be made.

(a) Formulate the LP model for this model with the non-negative constraints as Xi => 0

(b) Develop this model in Excel and copy paste the model in your answer sheet showing the formulae clearly.

(c) Solve this problem and recommend the optimal number of speedboats and pontoons to make and the maximum revenue.

(d) Explain why answers proposed in (c) cannot be implemented by the producer of the boats.

(e) Propose a better solution to the producer of the boats that can be implemented by the producer. State the number of speedboats and pontoons and revenue for this new proposal.

(f) All balance materials at the end of the seasons will be sold as scrap at a price of $10 per meter for board and $12 per square meter for fiberglass. Calculate the value of scrap sold at the end of the season if proposal (e) is implemented.

2. Derek's Transport is to move goods from two factories to three distribution centers at minimum costs. The supply from factories A and B are 30 units and 20 units respectively. The demand from distribution centers P, Q and R are 25 units, 15 units and 10 units respectively. Transport costs are shown in the Table 1.

Transport Cost in $

P Q R

A 14 9 7

B 8 10 5

Table 2: Transport Cost in $

(a) Develop the network model of the distribution system.

(b) Develop the linear programming model. (use the Xij notation to define your variables)

(c) Develop the excel model for this problem and copy paste the model in your answer sheet showing the formulae clearly.

(d) Fill up table 2 below showing clearly the quantities transported from each factory to each distribution centers and the minimum total transportation costs.

Quantity Shipped

P Q R

A ? ? ?

B ? ? ?

Table 2

Total Transportation costs =

e)The temporary bridge built on route BR can only handle a maximum weight of 10 units. Write the new LP model for this new problem and solve this problem. Copy and paste the excel model. Fill table 3 below with the quantity shipped and the total transportation cost.

Quantity Shipped

P Q R

A ? ? ?

B ? ? ?

Table 3

Total transportation costs =