# Linear Programming

posted by on .

I really really need help with this question, i've tried it different ways and end up confusing myself more. It's a multi schedule question and my biggest block is coming up with the objective function. HELP!!!

The Homespun Company produces an air conditioning unit for use in vehicles. The company has firm orders for six months in the future. The company can schedule its production over the next six months to meet these orders in either a regular (<=500 units per month) or an overtime (<=300 units per month) Customer orders and associated production costs for the next six months are as follows:

Cost (\$per Unit)
MONTH ORDERS REGULAR OVERTIME

Jan 590Units \$50 \$62
Feb 610Units \$52 \$58
Mar 650Units \$51 \$63
April 700Units \$55 \$60
May 500Units \$47 \$55
June 700Units \$50 \$52

At the beginning of Jan, the company has 75 units in inventory. At the end of June it wishes to have at least 100 units in inventory. The inventory carrying cost for the air conditioners is \$10 per unit per month. Formulate as linear programming model.