A factory produces tires of type A and B. In the next three months it needs to produce tires to meet the following demand (in number of tires per month): Type A Type B
Month 1 16000 14000
Month 2 7000 4000
Month 3 4000 6000
To produce these tires the factory uses two production lines, L1 and L2. L1 and L2 works in parallel, i. e., to complete one tire, the raw material needs to be processed by one of the two lines only (not both). Each line is available every month for the following working hours
L1 L2
Month 1 2000 3000
Month 2 400 800
Month 3 200 1000 The processing time to produce one tire is different for the two lines and depends of the type of tire, as reported below (in hours)
L1 L2
Type A 0.10 0.12
Type B 0.12 0.18
The labor cost on each line is equal to $6000 per hour. The cost of the raw material necessary to produce one tire is $2500 and $4000 for type A and type B, respectively.
In the first and second month one can produce more than the required demand; the extra production will be stocked to be used the next month. The stocking cost is $350 per tire. It is assumed that there is no inventory available at the beginning of the first month and there must be no tires in the inventory at the end of the last month. Formulate a Linear Programming planning the production of tires in the three months minimizing the cost of the entire production. Integrality constraints can be neglected.