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 works on order he will be paid _, 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 , the travel cost for technician , the payment _, if technician works on order and the sign means that technician cannot work on order .

Orders				Technicians							Revenue in thousands
	1	2	3	4	5	6	7	8	9	10
1	200			200	300			200
2		200	400				200			300
3	300					200		250	150
4		200	400		250					200
5	200					200	150		150
6		200		200				150		200
Travel cost	800	500	600	700	800	600	400	500	400	500

	Problem 1 Parameters
Group #	R1	R2	R3	R4	R5	R6
1	12	10	8	6	9	15