Problem 1: A machine shop received job orders from 6 customers to manufacture items that require highly skilled technicians. The shop does not have permanent skilled workers. It will hire technicians to work on these orders based on their expertise. Ten skilled technicians are available to choose from. If technician i works on order j he will be paid ri,j as shown in the table below. Each order requires a specific team of technicians. Because of time limitations, a technician can work in at most two orders. The company does not have to accept all the orders. The table shows the revenue of each order. If a technician is selected, he will be flown to Dhahran at the expense to the shop. Formulate an integer program that maximizes the profit of the shop (revenue minus payments to workers and travel cost). The solution should give the orders to be accepted and the technicians to be hired. Note that the numbers in the table present the revenue per order j, the travel cost for technician i, the payment ri,j if technician i works on order j and the sign "_" means that technician i cannot work on order j. Orders 1 2 3 4 Technicians 5 6 7 8 9 10 Revenue in thousands - 1 2 3 4 200 - 300 - - 200 200 400 400 - - - - 200 - 200 300 - - 200 - - R - - 300 R - 250 - 200 200 - 250 150 - R3 - - 200 R4 5 200 - - 150 - 150 - Rs 6 - 200 - 200 - - 150 - 200 R6 Travel 800 500 600 700 800 600 400 500 400 500 cost