Calc help please: Applied Max/Min please!!

Question

Applied Max/Min (25 points)
a. You have $2000 dollars to buy fence to enclose a
rectangular plot of land (see figure at right). The
fence for the top and bottom costs $5 per foot and
for the sides it costs $3 per foot. Find the
dimensions, x and y, of the plot with the largest
area. For this largest plot, how much money was
used for the top and bottom, x, and for the sides,
y?












b. You have T dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence
for the top and bottom costs $5 per foot and for the sides it costs $3 per foot. Find the dimensions of
the plot with the largest area. For this largest plot, how much money was used for the top and
bottom, x, and for the sides, y?











c. You have T dollars to buy fence to enclose a rectangular plot of land. The fence for the top and bottom
costs $A per foot and for the sides it costs $B per foot. Find the dimensions of the plot with the largest
area. For this largest plot, how much money was used for the top and bottom, x, and for the sides, y?

Answer 1

$10 X + $6 Y = $2000 equation 1

10X represents both the top and bottom cost of the fence, and 6Y is the cost of both sides of the fence. We want to use up the entire 2000 dollars.

Isolating Y we have Y = --1.67X + 333.33

Multiply X and Y to get --1.67X^2 + 333.33X

Differentiate to get --3.34X + 333.33, and equate this to zero.

Solve for X to get --333.33 / --3.33 = 100 feet

Plug this into equation 1 and solve for Y to get 166.67 feet.

So we have X = 100 Feet, and Y = 166.67 Feet

Area will be X times Y or 16,667 square feet.

Top and bottom fencing will cost $1000, sides will cost $1000.

 

Use this logic and format to solve for your other questions( b and c).