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(7 pts) Formulate this problem with a network representation. What type of network problem does this correspond to?(6 pts) What are the constraints of the corresponding LP formulation.(6 pts) Suppose now that in addition to purchase cost, the company also faces maintenance costs. Maintenance costs depend on the age of the truck, and are as shown inthe following table:Truck Age1234Maintenance Cost1.5357.5How does this change your network representation?I J1234061527421-1023362--11253---15
a)b) What are the constraints of the corresponding LP formulation.X01 + X02 + X03 + x04 = 1X01 = X12 + X13 + X14X02 + X12 = X23 + X24X03 + X13 + X23 = X34X04 + X14 + X24 + X34 = 1c) Suppose now that in addition to purchase cost, the company also faces maintenance costs. Maintenance costs depend on the age of the truck, and are as shown in the following table:Truck Age1234Maintenance Cost1.5357.5How does this change your network representation?012346232510111527364215012347.527.529.511.512.516.536.547.55919.5
Question 5(16pts): Integer ProgrammingThe Research and Development division of a company has been developing five possible new product lines. Management must now make a decision as to which of these five products actually will be produced and at what levels. A substantial cost is associated with beginning the production of any product, as given in the first row of the following table. Management's objective is to find the product mix that maximizes the total profit (total net revenue minus start-up costs).Product12345Start-up cost$50,000$40,000$70,000$60,000$85,000Marginal revenue$70$60$90$80$75Management has imposed the following restrictions on the variables:No more than three of the products can be produced;Products 3 and 4 are mutually exclusive and so are products 1 and 2. Furthermore,neither product 1 nor product 2 can be produced unless either product 3 or product4 is undertaken.If product 2 and product 3 are not produced, then product 5 must be produced.In addition, management has two possibilities for the production of the chosen products. It can produce in Factory A, in which 6000 labor hours are available, or in Factory B, in which 6500 labor hours are available. The per unit labor requirements (in hours) are given in the following table:Product12345Factory A53646Factory B46354For administrative reasons management wants just one the factories to be chosen. The plant chosen should be the one that provides the most profitable product mix.