Mrs. Jones always wanted a white picket fence in front of her house. Mr. Jones, her husband, wants a fence around the entire house including a decently-sized lawn in the front and a garden in the back. The fence border should look like a rectangle (see picture above). He calculated that he would need to fence off an area of 4,000 square feet in order to fit all these things. He wants to appease his wife and at least build the white picket fence in front of the house. He plans to build the rest of the fence with chain link, a cheaper material. Given that a white picket fence costs $7 per foot and a chain link fence costs $4 per foot, what dimensions for the entire area will give the cheapest cost for the entire fence

The dimensions for the entire area will give the cheapest cost for the entire fence are 40 feet in front, 100 feet on each side, and 40 feet on bottom.

Explanation:

Since Mrs. Jones always wanted a white picket fence in front of her house, and Mr. Jones, her husband, wants a fence around the entire house including a decently-sized lawn in the front and a garden in the back, and the fence border should look like a rectangle, and I have calculated that he would need to fence off an area of ​​4,000 square feet in order to fit all these things, and he wants to appease his wife and at least build the white picket fence in front of the house, and he plans to build the rest of the fence with chain link, a cheaper material, given that a white picket fence costs $ 7 per foot and a chain link fence costs $ 4 per foot, to determine what dimensions for the entire area will give the cheapest cost for the entire fence, the following calculation should be performed:

Area of ​​a rectangle = base times height = Z x Y = 4,000

80 x 50 = 4,000

40 x 100 = 4,000

20 x 200 = 4,000

20 x 7 x 2 + 200 x 4 x 2 = X = 280 + 1600 = 1880

40 x 7 x 2 + 100 x 4 x 2 = X = 560 + 800 = 1360

80 x 7 x 2 + 50 x 4 x 2 = X = 1120 + 400 = 1520

Therefore, the dimensions for the entire area will give the cheapest cost for the entire fence are 40 feet in front, 100 feet on each side, and 40 feet on bottom.