Problem # Line up equation: y = ax² + bx+c Y = x² +3 List values: a= b= CH smiling/frowning minimum/maximum Axis of Symmetry: X= -b 2a Vertex: Plug in x-value to find y. Vertex=(. ) X Y (x, y) Chart: y = a(x)² + b(x) ← Vertex
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- Feasible region all part of this problem refer to the following Feasible region and objective function. {x0xyx+2y12x+y10}P=x+4y (a) Graph the Feasible region. (b) on your graph from part(a) , sketch the graph of the linear equation obtained by (c setting P equal to 40,36,32 and 28 . (c) if you continue to decrease the value of P, at which vertex of the Feasible region will these lines first touch the Feasible region . (d) verify that the maximum value of P on the Feasible region occurs at the vertices you too chose in part(c).You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 4 eggs and 2 cups of cream. Into each quart of Continental Mocha go 4 eggs and 1 cup of cream. You have in stock 2000 eggs and 800 cups of cream. Draw the feasible region showing the number of quarts of vanilla and number of quarts of mocha that can be produced. (Place Creamy Vanilla on the x-axis and Continental Mocha on the y-axis.) Find the corner points of the region. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) (x, y) = (x, y) = (x, y) = (x, y) =Use Lagrange multipliers to find the maximum volume of a box inside a sphere of radius 12cm. -Make a diagram that illustrates the problem statement -shows and explains the equation to maximize and the restriction equation -develop the lagrange multipliers and solve the system -displays the result of the variables and defines the maximum volume
- This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y) = x2 − y2; x2 + y2 = 49 Maximum Value=? Minimum Value=? Thank YouThis extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y) = x2 − y2; x2 + y2 = 49 maximum value ? minimum value ? Please Help find Maximum and minimum value.the graph of y = 1/2 + (x2 - 2x + 1)/(x2 - 2x + 2) for 0 … x … 2. Find the coordinates of the minimum point.
- Ol’-Time Quilts receives an order for a patchwork quilt made from square patches of three types: solid green, solid blue, and floral. The quilt is to be 8 squares, and there must be 15 times as many solid squares as floral squares. If Ol’-Time charges $3 per solid square, $5 per floral square, and if the customer wishes to spend exactly $300, how many of each type of square may be used in the quilt? Give a general solution stating any limitation on the parameter. Then provide two specific solutions and compare. Is one of those two solutions preferable over the other? If so, why might be the case? If not, why are the two specific solution equally preferable?34) Maximize Z = 3x + 4y subject to the constraints: × + y <= 4, ×>=0, y =0. Find the maximum value of 2?2. Apply the graphical approach to minimize the cost function: C(x, y) = x + y Subject to the constraints: A. 2x + y ≤ 16 B. -2x+y≤4 C. x+y≥4 D. x
- Maximize the objective function subject to the constraints 3x + y ≤ 15, 5x + 3y ≤ 33, x ≥ 0, and y ≥ 0. (If the maximum value occurs on a segment, enter any point on that segment.) z = 3x + y The maximum value is at (x, y) = _________Maximize z = 3x + 4y, subject to the following constraints. (See Example 9.)−3x + y ≤ 33x − 6y ≤ 12x ≥ 0, y ≥ 0maximum value (Enter an exact number. If an answer does not exist, enter DNE.)z = The maximum value is at the following point. (Enter your answer as an ordered pair in the form x, y.)(x, y) =Solve with graphical methoda) Min F=x^2 + y^2 S.t x+y≤10 x+y≥5 2x+y≤15 x,y≥0 b) "Optimum point of a linear programming problem always lies on one of the corner points of the graph’s feasible region" Does this also apply to nonlinear programming ?If not Explain how to get a nonlinear programming answer (max , min) from a graph. #graphical_method_in_nonlinear_programming