Suppose i want to build a garden abutting my house, using the house as the west side of the garden. the south and east sides of the garden will face the street, so there i will use a decorative wall costing $30 per foot. the north side of the garden will use a tasteful fence, costing $20 per foot. if i want a 540 square foot garden, what is the minimum it will cost me?

Step-by-step explanation:

Let  l be the length of west side and w be the length of north side.

   East side = West side = l

   North side = South side = w

   Area = lw = 540 ft²

   We have

 Cost for fencing

             C = 30 w + 30 l + 20 w = 30 l + 50 w

At minimum cost derivative is zero,

That is

We have

                 lw = 540

                30 x w =540

                   w = 18 ft

Cost = 30 l + 50 w =30 x 30 + 50 x 18 = 1800 $

Minimum cost is 1800 $

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!