Hint: For this question you may find it helpful to remember that a2-62(a+b). (a−b). = For subject to find a. F(x,y)=4x-y-24(x + y) x² + y² = 36, a global maximum stationary point and its value; Maximum point: (x, y)max = ab sin (a) Show/hide Maximum value: F(x,y)max = f əx 8
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- Solve the given optimization problem by using substitution. Find the minimum value of f(x, y, z) = 2x2 + 2x + y2 − y + z2 − z − 1 subject to z = 2y. fmin = Also find the corresponding point (x, y, z) =Solve the given optimization problem by using substitution. Find the minimum value of f(x, y, z) = 2x2 + 2x + y2 − y + z2 − z − 9subject to z = 2y. fmin = Also find the corresponding point (x, y, z).Minimize ?=2x+3y subject to: 4x+y≥7 x+y≥4 2x+5y≥14 x, y≥0 Corner points at _______________________________ Minimum value of ___________ at x = __________ and y = ____
- maximize p=10x+65y x+6y≤12 x≥0 y≥0 What is the maximum value of P? What are the coordinates of the corner point where the maximum value of P occurs?Solve the given optimization problem by using substitution. Find the minimum value of f(x, y, z) = 2x2 + 2x + y2 − y + z2 − z − 5 subject to z = 2y. fmin= (x, y, z) =Experiments show that the quantities x of corn and y of soybean required to produce a hog of weight Q satisfy Q = 0.5x1/2y1/4. The unit of x, y, and Q is the cwt, an agricultural unit equal to 100 lb. Find the values of x and y that minimize the cost of a hog of weightQ = 2.5 cwt if corn costs $3/cwt and soy costs $7/cwt.
- Experiments show that the quantities x of corn and y of soybean required to produce a hog of weight Q satisfy Q=0.5x1/2y1/4 The unit of x, y, and Q is the cwt, an agricultural unit equal to 100 lb. Find the values of x and y that minimize the cost of a hog of weight Q=2.5 cwt if corn costs $4/cwt and soy costs $18/cwt.A company produces x units of product A and y units of product B ( both in hundreds per month ). The monthly profit equation ( in thousands of dollars ) given by P ( x, y ) = -4x2 + 4xy - 3y2 + 4x + 10y + 81 A ) Find Px ( 1 , 3 ) and interpret the results. B ) How many of each product should be produced each month to maximize profit ? What is the maximum profit ?Minimize f(x,y,z) = 3x2+4y2+6z2 subject to the constraint 3x+7y+8z=20. a.) When the minimum occurs, what is x? b.) When the minimum occurs, what is y? c.) When the minimum occurs, what is z? d.) What is the minimum value of f(x,y,z)?
- Solve what it says in the image using lagrange multipliers, putting what is being done step by step. Consider the function f(x,y)= 8x2-8xy+2y2 Using Lagrange multipliers find the extremes of f(x,y) subject to the constraints x2+y2=10Use the EVT to find the maximum and minimum values of the function f(x,y)=−4x2y+4xy2 on the square 0≤x≤2, 0≤y≤2. What is the maximum value of f(x,y)? Find the point(s) at which f(x,y) is a maximum: What is the minimum value of f(x,y)? Find the point(s) at which f(x,y) is a minimum:Demand for apartments in a certain town is D(x)=1480−3x,and the supply is S(x)=500+11x, where x is the number of apartments, in hundreds, and D(x) and S(x) are the rent in dollars per month, per apartment. a) Find the equilibrium point = b) Find the consumer surplus and producer surplus= c) Suppose a maximum rent of$1050 per month is imposed by the town council. Find the point xC, pC= d) Find the new consumer surplus and new producer surplus= e) Find the deadweight loss=