Preface: In this discussion we will do a brief introduction to the gradient descent method.Formulas: Method of Lagrange Multipliers.To find the absolute max/min values of a differentiable function f(x,y) subject to the domain restriction g(x,y)=0;Find values of x and y such thatgradf(x,y)=gradg(x,y), and ,g(x,y)=0Evaluate f at the values (x,y) found in step 1 and at any endpoints of the curve g(x,y)=0 to determine the locations of the absolute maxmin values.Problem 1: The golf ball manufacturer, Pro-T, has developed a profit model that depends on the number x of golf balls sold per month (measured in thousands), and the number y of hours per month of advertising, according to the functionp(x,y)=48x96y-x2-2xy-9y2where p is measured in thousands of dollars. Budgetary constraints give rise to a cost function relating the production of thousands of golf balls and advertising units, given byy=54-5xManufacturing costs of the golf balls themselves also limit their availability to at most 10,800 per month. Your goal is to find the values of x and y that maximize the profit, and find the maximum profit.(a) What is the objective function?(b) What is the constraint g(x,y)=0?(c) What are the constraints on the variable x?(d) Does the Extreme Value Theorem apply to this situation? Your answer should mention the endpoints of the constraint curve.(e) Find the values of x and y that maximize the profit, and find the maximum profit. Round any computations to two decimal places. Don't forget to test the endpoints of the curve.