Q4. (2,3) is a saddle point since min is row is equal to max in column at this point
So it is optimal for player A to chose II and Player B to chose III
Q5. (12x^2 - 45x +40)x^2 + 5
since max value depends on max value of quadratic i.e. infinite since it's in upright parabola
min value depends on min value of quadratic i.e. when derivative is zero
24x -45 = 0 => x = 15/8
so min value is f(15/8) DIY
Q4: Solve the payoff matrix Example-1 Player B П I III IV V -2 0 0...
Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the maximum value of f(x, y) = xy subject to x + 2y = 72. Fmax = Also find the corresponding point (x, y). (x, y) = (1
Please answer both 4. 0-2 points TanFin1 14.1.022 Solve the linear programming problem by the simplex method. Maximize P 12x + 9y subject to x+ys 12 3x ys 30 10x + 7y 70 x 20, y 20 The maximum is P at (x, y)- Submit Answer Save Progress 5. -12 points TanFin11 4.1.028. Solve the linear programming problem by the simplex method. Maximize P2z subject to 2x y + zs 12 4x +2y 3z s 24 2x + 5y 5z...
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks] (c) Use Lagrange Multiplier to find the absolute maximum and minimum of 10 (x,y)-x +y subject to 2 12 marks 6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks]...
Calculus III 1) Identify each of the following surfaces: а) z' %3x? - 5у" b) z 4x2-4 y c) z2+3x2-5y = 4 d) z2x23-5y e) у3х* 2) Find and classify all of the critical points for f(x, y)=xy -x2 + y'. 3) Find the maximum and minimum values of f(x,y)=xy over the ellipse х* + 2y %3D1. 4) Let fx, y) x3 -cosy a) Find the first order Taylor polynomial for f(x,y) based at (1,7). b) Find the sccond order...
Calculus 4 Let f(x,y) = A)-i-j E) i+j 1. Find the gradient vector Vf (1, 1) at the point (x,y) = (1,1). B) - 1 - 1 D)-i-j 10. . Find the largest value of the directional derivative of the function f(x,y) = ry + 2ya at the point (3,y) = (1,2). A) 53 ' B) V58 C) V63 D) 74 E) 85 y + The function (,y) = 2 + y2 + A) (-3,5), saddle point C) (-1,3), maximum...
Score: 0 of 2 pts Question Help 15.8.11 The function f(x,y) = 5xy has an absolute maximum value and absolute minimum value subject to the constraint x² + y2 - xy = 9. Use Lagrange multipliers to find these values The absolute maximum value is SHA re b-a. Cryou the box and then click Check An 1
help me 1 Solve the egua rim : y" - 2y' + 2y 0• (20) 2 Solve the equotion: y" - 4y' + 5y = 0 y(0) = 2 y'(0)= 6 • (20) 3 Solve the linear system: (20) X, +2x2 + 3x, = 7 2x, + 5x, + 3x3 = 12, %3D X1+ 0x2 + 8x3 = 10 4 Pind the eigenvəlues, and eiyenvectors (20) 4 -1 5 Find the relation ship between x and y. (20) Y=ax+b, a=?,...
For each of the following systems, find a > 0 and b > 0 such that L(x, y) = ax^2 + by^2 obeys d/dt(L) not = 0 whenever (x, y) 6= (0, 0). (This makes L a Liapounov function.) State whether the origin is a stable or unstable equilibrium in each case. (a) x' = −x^3 + 7xy^2 , y' = −3x^2y + y^3 . (b) x' = x^3 − y^3 , y' = 3xy^2 + 4x^2 y + 5y^3...
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval (-3, 2] 3-X b) Find the absolute maximum and minimum values of function f(x)= (1+x?)Ě over the interval [-1,1] c) Find the following for the function f(x) = 2x – 3x – 12x +8 i) Intervals where f(x) is increasing and decreasing. ii) Local minimum and local maximum of f(x) iii) Intervals where f(x) is concave up and concave down. iv) Inflection point(s). v)...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....