2 operation research new Q

Formulate the following linear program

CLEARLY IDENTIFY YOUR VARIABLES. THE FORMULATION SHOULD BE WRITTEN IN A FORM READY FOR INPUT (i.e. variables on the left and constants on the right).

A company wants a high level, aggregate production plan for the next 6 months. Projected orders for the company's product are listed in the table. Over the 6-month period, units may be produced in one month and stored in inventory to meet some later month's demand. Because of seasonal factors, the cost of production is not constant, as shown in the table.

The cost of holding an item in inventory for 1 month is $4/unit/mo. Items produced and sold in the same month are not put in inventory. The maximum number of units that can be held in inventory is 250. The initial inventory level at the beginning of the planning horizon is 200 units; the final inventory level at the end of the planning horizon is to be 100. The problem is to determine the optimal amount to produce in each month so that demand is met while minimizing the total cost of production and inventory. Shortages are not permitted.

	Demand	Production
Month	(units)	cost ($/unit)
1	1300	100
2	1400	105
3	1000	110
4	800	115
5	1700	110
6	1900	110

Formulate the following linear program

CLEARLY IDENTIFY YOUR VARIABLES. THE FORMULATION SHOULD BE WRITTEN IN A FORM READY FOR INPUT (i.e. variables on the left and constants on the right).

CSL is a chain of computer service stores. The number of hours of skilled repair time that CSL requires during the next five months is as follows:

January	6,000 hours
February	7,000 hours
March	8,000 hours
April	9,500 hours
May	11,000 hours

At the beginning of January, 50 skilled technicians work for CSL. Each skilled technician can work up to 160 hours per month. To meet future demand, new technicians must be trained. It takes one month to train a new technician. During the month of training, a trainee must be supervised for 50 hours by an experienced technician. Each experienced technician is paid $2,000 a month (even if he or she does not work the full 160 hours). During the month of training, a trainee is paid $1,000 a month. At the end of each month 5% of CSL’s experienced technicians quit to join Plum Computers. Formulate (do not solve) a linear program whose solution will enable CSL to minimize labor cost incurred in meeting the service requirements for the next five months