Mixture Problems A 1500 gallon tank initially contains 600 gallons of water with 5 lbs of salt dissolved in it. Water enters the tank at a rate of 9 gal/hr and the water entering the tank has a salt concentration of (1+cos(t)) Ibs/gal. If a well mixed solution leaves the tank at a rate of 6 gal/hr, how much salt is in the tank when it overflows? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the Volume Equation 3. Settimg Up the differential equation 4. Listing down initial Conditions 5. Plugging in Conditions. 6. Finding the resulting model 7. Finding the concentration when the tank overflows 8. Graph the solutions

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Linear Programming Concepts

Linear programming is a famous mathematical modeling tool for determining the best distribution of scarce resources among competing demands. Machinery, time, personnel, raw materials, money, and space are all resources. It is used to find the most optimal solution to a problem with given constraints. The real-life situations can be formulated using linear programming concepts into a mathematical model. Linear programming problems consist of an objective function and linear equalities subjected to constraints.