I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, while the fencing for the north and south sides costs only $3 per foot. I have a budget of $120 for the project. What is the largest area I can enclose ?
A)12 square feet
B) 150 square feet
C) 120 square feet
D) 300 square feet
E) 75 square feet

Question

I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, while the fencing for the north and south sides costs only $3 per foot. I have a budget of $120 for the project. What is the largest area I can enclose  ?
A)12 square feet
B) 150 square feet
C) 120 square feet
D) 300 square feet
E) 75 square feet

Quizplus · Accepted Answer

To maximize the area, let the length of the north and south sides be x and the length of the east and west sides be y. The cost equation is 3x + 4y = 120. The area A = xy. Solving for y in terms of x gives y = (120 - 3x)/4. Substituting into the area equation gives A = x(120 - 3x)/4. To maximize A, take the derivative and set it to zero, solving gives x = 20, y = 15, thus the area is 75 square feet.

I Want to Fence in a Rectangular Vegetable Patch