2 Optimal garden A rectangular flower garden with an area of 30 m is surrounded by a grass border 1 m wide on two sides and 2 m wide on the other two sides (see figure). What dimensions of the garden minimize the combined area of the garden and borders?

Solution Step 1: 2 We have given a rectangular flower with an area of 30m and is surrounded by a grass border 1 m wide on two sides and 2 m wide on the other two sides the diagram as shown below Step 2: We have to determine the dimensions the garden and minimize the combined area of the garden and borders Let the sides of the rectangular garden be x and y 30 Area of the rectangular garden is constraint xy=30 y = x ….(1) since border of the garden is 1m wide on two sides.Let’s assume that border of the garden is 1m wide on each side of y then similarly assume that border of the garden is 2m wide on other each side of x so the area of the grass border is 2y+4x