A mining company extracts gravel, the basic product it sells, from three mines, L1, L2 and L3. The weekly production of each mine is 75, 150 and 75 tons of gravel respectively. The gravel has to be transported to five main consumers, K1, K2, K3, K4 and K5 requiring for their needs 100, 60, 40, 75 and 25 tons of gravel per week respectively. The problem that concerns the company's management is the minimization of the required cost for the transportation of the product to the consumers. For this purpose a detailed cost analysis was carried out which gave the results of the following table (the numbers denote the transportation cost in per ton of gravel). K1 K5 3 1 4 2 1 2 1. Write the transportation model and the transportation tableau. 2. Use Excel to find the optimal solution for this problem. Mines Customers K3 3 2 5 L1 L2 L3 K2 2 1 0 K4 4 4 3 Use the branch-and-bound method to find the optimal solution to this Integer Programming problem max s.t Z = 4x + x 2x + x 5 2x + 3x 5 (X X) 20; X, X2 Integer NTC is a small business that receives checks from all over Cote d'Ivoire. The average daily total payments mailed by customers from each region of Cote d'Ivoire to NTC is as follows: the West, 70000 CFA Francs; the North, 50000 CFA Francs; the East, 40000 CFA Francs; the South, 60000 CFA Francs. NTC must decide where customers should mail their payments. Because NTC can earn 20% annual interest by investing these revenues, NTC would like to receive payments as quickly as possible. NTC is considering setting up operations to process payments in four cities: Abidjan, Abengourou, Korhogo, and Man. The average number of days from the time the is sent until it is cleared and deposited in NTC bank account depends on the city to which the payment is mailed, as shown in the table below. Region 1: West Region 2: North Region 3: East Region 4: South City 1 Man 268 8 City 2 Korhogo 625 2 5 5 City 3 Abengourou 8525 2 5 City 4 Abidjan 8 5 5 2 The annual cost for the payment processing office in a city is 50000 CFA Francs. In addition, if customers in Region 1 (West) send their checks to City 1 (Man), then no other customers from the other regions may sent their payments to City 1. 1. Formulate an Integer Programming model that NTC can use to minimize the sum of the costs due to lost interest income and running a payment processing office. 2. Use MS Excel to find the optimal solution to this IP problem.