During the next four months Capps Shoes Company must meet the following demand for pair of shoes: 2000 shoes in month 1, 3000 shoes in month 2, 4000 shoes in month 3, and 5000 shoes in month 4. At the beginning of month 1, 500 shoes are on hand. This company has 100 workers. A worker is paid $11.5 per hour in month 1, $11 per hour in month 2, $10.5 per hour in month 3, and $10 per hour in month 4. Each worker can work up to 160 hours in month 1, 150 hours in month 2, 140 hours in month 3, and 160 hours in month 4 before he or she receives overtime. Each worker can work up to 20 hours overtime per month and is paid $13 per hour for overtime labor. It takes four hours of labor and $15 of raw material to produce a pair of shoes. At the end of each month, a holding cost of $3 per pair shoes left in inventory incurred. During all these four months, the option of buying form a subcontractor is also available. Buying a pair of shoes from the subcontractor costs $80 and its current capacity is 200 shoes per month. Currently, production in a given month can be use to meet that same months demand and the following months demands. The company wants to determine its optimal production schedule.

Let Rij, Oij, Sij represent the number of shoes prepared from production in regular hours, production in overtime, and bought from the subcontractor in period i and is sold in period j, respectively.

1. How many pair of shoes need to produce during the regular hours in month 1, 2, 3, and 4 to minimize total cost? (show where you get that information on the answer report as well as providing the answers below).

R1= R11+ R12 + R13 + R14=

R2= R21 + R22 + R23 + R24=

R3= R31 + R31 + R33 + R34=

R4= R41 + R42 + R43 + R44=