Fill in the blanks: The goal of an optimization problem is to find the maximum or minimum value of the ________function subject to the ________.

Solution Step 1: In optimization problem we are looking for the largest value or the smallest value that the function can take those functions are call objective functions.objective function is used in optimization.it denotes the function to minimize or maximize.The constraint will be some condition that can usually be described by some equation.in other words we can say that in optimization problem used to maximize some function where the input variables are restricted in some way those restrictions are the constraints . The goal of optimization problem is to find the maximize or minimum value of the objective function subject to the constraints The goal in optimization is to find the best decision variables values that satisfies all constraints. Hence the blanks are filled with objective function and constraints For example A farmer has 3400 feet of fencing and wants to fence off a rectangular field that borders a straight river;he needs no fence along the river. The area of the rectangular field that maximize is denoted as, . The constraints in this case is 2x+y=3400 Use this constraint to solve the optimization problem. Solve the second equation for and substitute the result into the first equation to express as a function of one variable.