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A stationary manufacturer produces two pen varieties, standard (S) and premium (P). These are packed and sold respectively at Rs. 10 and Rs. 25. Two machines, M1 and M2, are available to produce both varieties. M1 can produce 30 and 50 pens (including refills) per minute of S and P respectively. M2 can produce 40 and 60 per minute of S and P respectively. The manufacturer runs two shifts of 8 hours each.
[1] The above partial information can then be formulated mathematically as
1). Max Z = 10S + 25P
Subject to:
70S ≤ 960
110P ≤ 960
S, P ≥ 0, and integers
(2) Max Z = 10S + 25P
Subject to:
S/70 ≤ 960
P/110 ≤ 960
S, P ≥ 0, and integers
(3) Max Z = 10S + 25P
Subject to:
S/30 + P/50 ≤ 960
S/40 + P/60 ≤ 960
S, P ≥ 0, and integers
(4) Max Z = 10S + 25P
Subject to:
30S + 50P ≤ 960
40S + 60P ≤ 960
S, P ≥ 0, and integers
[2] The manufacturer also ensures that at any time at least 80 more and 50 more refills (R) are produced for S and P, respectively. The same refill is used for S and P. This constraint can be specified as
(1) R = 130
(2) R − (S + P) ≥ 130
(3) R = 80 + S, R = 50 + P
(4) R ≥ 130asked in JMET
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