Let x₁ be the number of machine part I X₂ be the number of machine part II Objective Function: Max P = 50x₁ + 100x2₂ subject to: 10x1 + 5x22500 4x110x22000 X₁ + 1.5x2 < 450 X1, X20 Solve the given LP Problem using simplex method and perform the sensitivity analysis. Find the optimality range.
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- Solve for the critical points and determine whether they are minimum point, maximum point or point of reflection. 1. y = 3x2 – 6x 2. y = x3 – 6x2 + 1 3. y = x3 – x2 – x 4. y = (x3–4)2/3 5. y = x4 + 1/x2 6. y = 1/4x4 – x3 + x27. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.Determine all local optimum points and all infection points. f(x) = x³+ 3x² - 9x - 3
- Find the minimum of the function f(x) = (X/log X) by using the quadratic-interpolation method with an initial trial step length as 0.1In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.Rather than order rabbit food that is custom-blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend?In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.Rather than order rabbit food that is custom‐blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend? a. Choose the unknowns, i.e. variables. Statewhat they are so you know exactly whatyou are looking for.b. Write your OPTIMIZATION EQUATION. c. Write the constraints as a system ofinequalities, usually there are several.d. Graph the system and identify thefeasibility region. e. Identify the corners of the feasibilityregion, which will be…
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