Maximum area rectangles Of all rectangles with a perimeter of 10 m, which one has the maximum area? (Give the dimensions.)

Solution Step 1: Consider a rectangle of width x and length y here area of rectangle(length *width) is the objective function denote it by A Thus the objective function A=xy And perimeter of a rectangle is the constraints that is 2(x+y)=10m Our goal is to find the dimension of a rectangle of a perimeter 10m which gives maximum area Step 2: The first step is to use the constraints 2(x+y)=10 to express the objective function.A=xy in terms of a single variable For this 2(x+y)=10 (x+y)=5 (x+y)=5 The first step is to use the constraint to express the objective function A in terms of a single variable either in x or y suppose we express the objective function in terms of x For this; Step 3: Substitute for y the objective function A becomes A=xy =x(5-x) 2 A=5x-x 0 x 5 Which is the function of single variable with A(0)=A(5)=0