Answer:
Explanation:
1)
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xij = barrels of component i used in grade j per day for i = A, B, C and j = R, P, D
2)
Max Z = 18 (x AR + x BR + x CR) + 25 (x AP + x BP + x CP) + 15 (x AD + x BD + x CD) – 9 (x AR + x AP + x AD) – 7 (x BR + x BP + x BD) – 10 (x CR + x CP + x CD)
or,
Max Z = 9 x AR + 11 x BR + 8 x CR + 16 x AP + 18 x BP + 15 x CP + 6 x AD + 8 x BD + 5 x CD
3)
Subject to,
x AR + x AP + x AD <= 6000
x BR + x BP + x BD <= 3000
x CR + x CP + x CD <= 4500
x Aj + x Bj + x Cj >= 5000 for j = R, P, D
x AR >= 30%*(x AR + x BR + x CR) or, 0.7 x AR - 0.3 x BR - 0.3 x CR >= 0
x BR <= 30%*(x AR + x BR + x CR) or, -0.3 x AR + 0.7 x BR - 0.3 x CR <= 0
x CR >= 30%*(x AR + x BR + x CR) or, -0.3 x AR - 0.3 x BR + 0.7 x CR >= 0
x CP >= 60%*(x AP + x BP + x CP) or, -0.6 x AP - 0.6 x BP + 0.4 x CP >= 0
x BD <= 50%*(x AD + x BD + x CD) or, -0.5 x AD + 0.5 x BD - 0.5 x CD <= 0
xAD >= 10%*(xAD + xBD + xCD) or, 0.9 xAD - 0.1 xBD - 0.1 xCD >= 0
xij >= 0 for i = A, B, C and j = R, P, D
