4. Pegamento Chemical is a company developing a new glue, comprising three main chem- icals (in...

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4. Pegamento Chemical is a company developing a new glue, comprising three main chem- icals (in addition to other chemicals which can be ignored). These chemicals are some- what interchangeable. The chemicals are referred to as x1, x2, and 13, are available in virtually unlimited quantities, and respectively cost (per liter) $25, $37, and $48. The company must produce at least 10,000 liters of the new glue, including at least 200 liters of each chemical. Further, the amount of 22 must be at least twice as much as x3. When mixed with water (available in unlimited quantities), the chemicals react and provide a nonlinear yield, such that the total quantity of glue obtained q is given by: q=x3-0.25x+0.1x2 +0.01x12 (a) Formulate a NLP that will minimize Pegamento's costs. Provide descriptive labels for your constraints. Assume Pegamento can buy fractional liters of chemicals. (b) Solve your model in part (a) using MATLAB's fmincon function. (c) Which of the four main assumptions of linear programming does the model in part (a) violate? Explain. 4. Pegamento Chemical is a company developing a new glue, comprising three main chem- icals (in addition to other chemicals which can be ignored). These chemicals are some- what interchangeable. The chemicals are referred to as x1, x2, and 13, are available in virtually unlimited quantities, and respectively cost (per liter) $25, $37, and $48. The company must produce at least 10,000 liters of the new glue, including at least 200 liters of each chemical. Further, the amount of 22 must be at least twice as much as x3. When mixed with water (available in unlimited quantities), the chemicals react and provide a nonlinear yield, such that the total quantity of glue obtained q is given by: q=x3-0.25x+0.1x2 +0.01x12 (a) Formulate a NLP that will minimize Pegamento's costs. Provide descriptive labels for your constraints. Assume Pegamento can buy fractional liters of chemicals. (b) Solve your model in part (a) using MATLAB's fmincon function. (c) Which of the four main assumptions of linear programming does the model in part (a) violate? Explain.