1. A car assembly plant makes two types of cars, named the Avalon and the Bonavista....

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1. A car assembly plant makes two types of cars, named the Avalon and the Bonavista. Each Avalon gives a profit of $2000, while each Bonavista gives a profit of $3000. They must make at least 250 Avalons. Each Avalon requires 3 labour-hours in Department 1, and 8 labour-hours in Department 2. Each Bonavista requires one labour-hour in Department 1, and 15 labour-hours in Department 2. Each week Department 1 is available for 3000 labour-hours, and Department 2 is available for 17,990 hours. At least 25% of the total production must be of Bonavistas. (a) Formulate a linear optimization model for this situation. Write every constraint in standard form (<, =, or ≥ a number), with a one or two word description of the purpose of the constraint. (b) Solve the model using a 1500 by 1500 grid, clearly indicating each constraint with a word description next to it, the feasible region, the trial and optimal isovalue lines, and the point of optimality. Compute the exact solution algebraically, and clearly state the recommenda- tion and the OFV. 1500 Bonavistas 1000 500 500 1000 Avalons 1500 1. A car assembly plant makes two types of cars, named the Avalon and the Bonavista. Each Avalon gives a profit of $2000, while each Bonavista gives a profit of $3000. They must make at least 250 Avalons. Each Avalon requires 3 labour-hours in Department 1, and 8 labour-hours in Department 2. Each Bonavista requires one labour-hour in Department 1, and 15 labour-hours in Department 2. Each week Department 1 is available for 3000 labour-hours, and Department 2 is available for 17,990 hours. At least 25% of the total production must be of Bonavistas. (a) Formulate a linear optimization model for this situation. Write every constraint in standard form (<, =, or ≥ a number), with a one or two word description of the purpose of the constraint. (b) Solve the model using a 1500 by 1500 grid, clearly indicating each constraint with a word description next to it, the feasible region, the trial and optimal isovalue lines, and the point of optimality. Compute the exact solution algebraically, and clearly state the recommenda- tion and the OFV. 1500 Bonavistas 1000 500 500 1000 Avalons 1500