(Solved): Please Answer the question a and b. Thank you 3. Two types of rock are mined in a quarry. "Softrock" ...

3. Two types of rock are mined in a quarry. "Softrock" has an density (mass divided by volume) of 5 Tonnes per cubic metre, and "hardrock" has a density of 8 Tonnes per cubic metre. Up to 350 Tonnes of softrock can be mined each hour, and independent of this, up to 450 Tonnes of hardrock can be mined each hour. The mined rock is crushed and then travels on a conveyor belt. (To avoid mixing the two types of rock they will crush one type of rock, then switch over to the other type, and then keep switching back and forth). The conveyor belt can handle up to 97 cubic metres of rock per hour. The crusher can handle up to 980 Tonnes per hour when crushing softrock, or up to 490 Tonnes per hour when crushing hardrock. The companyy makes \$20/Tonne for softrock and \$30/Tonne for hardrock. The quarry operator wishes to know how many Tonnes of each type of rock they should produce each hour. (a) Formulate a linear optimization model for this problem. (b) Solve the model from part (a) graphically, clearly indicating the feasible region, and both the trial and optimal isovalue lines. Use algebra to determine the exact solution.