Let x1, x2 and x3 be no of items produced of A,B and C respectively
Profit per unit for A = Selling price – RM cost – Variable cost = 21 – 9 – 5 = 7
Profit per unit for B = 30-12-8 = 10
Profit per unit for C = 42-18-10 = 14
So total profit z = 7x1 + 10x2 + 14x3
Further, machinery time required by A, B and C are 1, 1.5 and 2 hrs respectively
So x1 + 1.5x2 + 2x3 <= 100 (since 100 machinery hours are available)
Also, craftsmen time required by A, B and C are 1.5, 2 and 2.5 hrs respectively
So 1.5x1 + 2x2 + 2.5x3 <= 140 (since 140 craftsman hours are available)
Further, company has specific contract to produce 12 items of B and B also has unlimited demand
i.e. x2 >= 12
Item C has a weekly demand of 10
i.e x3 <= 10
Item A has unlimited weekly demand
i.e. x1 >=0
Also, x1, x2, x3 >= 0
Hence the problem is formulated below:
Maximize 7x1 + 10x2 + 14x3
Subject to
x1 + 1.5x2 + 2x3 <= 100
1.5x1 + 2x2 + 2.5x3 <= 140
x2 >= 12
x3 <= 10
x1, x2, x3 >= 0
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