A crushing process in a quarry can be operated in three different scenarios which can generate the following products for every 100 tons of raw stone size >50 mm. 

The quarry received an order to provide the necessary crushed aggregate material for a large concrete pour of 1000 m3. The concrete mix design has the following stone requirements: 

• 19 mm stone 835 kg/m3 

• 13 mm stone 220 kg/m3 

• Crusher sand 662 kg/m3 

Your tasks include the following: 

A1: Form the system of linear equations. 

A2: Write the equations in a matrix form. 

A3: Generate the necessary program commands to calculate the number of materials (tons of > 50 mm stones) to be crushed using scenarios 1, 2 and 3 to cater for the concrete pour needs. 

A4: Do manual calculations/ or another online tool to appraise the results obtained in A3. 

A5: Use your findings in A3/A4 to advise the quarry manager on the best scenario/s to adopt for this job.

Crushing 19 mm stone 13 mm stone Crusher sand scenario (ton) (ton) (ton) Scenario #1 15 30 55 Scenario #2 35 50 15 Scenario #3 60 20 20