At the end of July, NWC wishes to have no recruits or apprentices but at least 140 full-time workers. Formulate and solve a linear program for NWC to accomplish this at minimum total cost.
National Wing Company (NWC) is gearing up for the new B-48 contract. Currently, NWC has 100 equally qualified workers. Over the next three months, NWC has made the following commitments for wing production:
Each worker can either be placed in production or train new recruits. A new recruit can be trained to be an apprentice in one month. The next month, he, himself, becomes a qualified worker (after two months from the start of training). Each trainer can train two recruits. The production rate and salary per employee are estimated below.
Pi = number of producers in month i (where i = 1, 2, or 3)
Ti = number of trainers in month i (where i = 1 or 2)
Ai = number of apprentices in month i (where i = 2 or 3)
Ri = number of recruits in month i (where i = 1 or 2)
Min 3000P1 + 3300T1 + 2200R1 + 3000P2 + 3300T2 + 2600A2 + 2200R2 + 3000P3 + 2600A3
s.t. 0.6P1 + 0.3T1 + 0.05R1 ? 20
0.6P1 + 0.3T1 + 0.05R1 + 0.6P2 + 0.3T2 + 0.4A2 + 0.05R2 ? 44
0.6P1 + 0.3T1 + 0.05R1 + 0.6P2 + 0.3T2 + 0.4A2 + 0.05R2 + 0.6P3 + 0.4A3 ? 74
P1 ? P2 + T1 ? T2 = 0
P2 ? P3 + T2 + A2 = 0
A2 ? R1 = 0
A3 ? R2 = 0
2T1 ? R1 ? 0
2T2 ? R2 ? 0
P1 + T1 = 100
P3 + A3 ? 140
Pj, Tj, Aj, Rj ? 0 for all j
P1 = 100, T1 = 0, R1 = 0, P2 = 80, T2 = 20, A2 = 0, R2 = 40, P3 = 100, A3 = 40
Total cost = $1,098,000
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