1. Simplex Method for BLENDING OF AGGREGATES The contract specifications of a building project require that the course aggregate grading for concrete mixing must be within the following limits: Sieve Size (mm)% passing by Weight 63.0100 37.595-100 20.035-70 10.010-40 5.00-5

2. BLENDING OF AGGREGATES The contractor has four quarry sites to supply aggregates. These aggregates, however, do not individually satisfy the above specifications requirement. The aggregate grading from each of quarry sites is shown below: Sieve Size (mm) % passing by Weight Quarry 1Quarry 2Quarry 3Quarry 4 63.0100 37.59095100 20.0506580100 10.00254090 5.000330 Transportation cost per tonne 12141011

3. BLENDING OF AGGREGATES The contractor needs to prepare 150 tonnes of aggregates for concrete mixing in the next two days. How should he obtain the aggregates from the quarry sites so that after blending them the aggregates will satisfy the specifications?

4. Solution Let X1, X2, X3 and X4 be the number of tonnes of aggregates supplied from quarry sites 1, 2, 3 and 4 respectively. The objective function: Minimize P = 12X1 + 14X2 + 10X3 + 11X4

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8. Solution The constraints for demand: X1+ X2 + X3 + X4 = 150 Also, X1, X2，X3， x4 ≥ 0 The solution for this model is given below: Total minimum costs = 1,690.16 X1 = 65.26 tonnes X2 = 10.04 tonnes X3 = 55.22 tonnes X4 = 19.48 tonnes