Shoeco: linear programming model to compute an optimal production policy

Part I
During the next four months Shoeco must meet, on time, the following demands for pairs of shoes: 300 in month 1; 500 in month 2; 100 in month 3; and 100 in month 4. At the beginning of month 1, 50 pairs of shoes are on hand, and Shoeco has three workers. A worker is paid $1500 per month. Each worker can work up to 160 hours a month before he or she receives overtime. A worker may be required to work up to 20 hours of overtime and is paid $25 per hour for overtime. It takes four hours of labor and $5 of raw material to produce a pair of shoes. At the beginning of each month workers can be hired or fired. Hiring costs are $1600 per worker and firing costs are $2000 per worker. At the end of each month, a holding cost of $30 is charged for each pair left in inventory. Production in a given month can be used to meet that months demand. Use LP to determine an optimal production and labor policy.

Part II
Assuming backlogs are allowed and that it costs $25 for each pair backlogged, adjust the above model to include that aspect.

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Month 1 Month 2 Month 3
Shoes Produced 360 390 120
Normal Labour Hours 1440 1440 480
Overtime Labor Hours 0 120 0
Raw Material Costs 1800 1950 600
Number of ...