Question

fence is to be built to enclose a rectangular area of 250 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 13 dollars per foot. Find the dimensions of the enclosure that is most economical to construct

Answer 1

Answer:

23.05 x 10.85

Step-by-step explanation:

Area of Rectangular Fence = L * W = 250$ft^{2}$

L * W = 250

W = $\frac{250}{L}$                                      ................................... (i)

Perimeter = 2L + 2W

Three sides cost 4 dollars per foot = 4(2L) + 4W

(The two lengths must be constructed with the 4 dollars materials)

Fourth side costs 13 dollars per foot = 13W

Cost = 4(2L) + 4W + 13W

C = 8L + 17W                         ...................................... (ii)

Substitute (i) into (ii)

C = 8L + 17 ($\frac{250}{L}$)

C = 8L + $\frac{4250}{L}$  

Plotting this equation with L on the x-axis and cost on the y-axis

minimum cost will be when L ≈ 23.05 ft

W = $\frac{250}{23.05}$ ≈ 10.85 ft

minimum cost = 8(23.05) + $\frac{4250}{23.05}$

minimum cost = 184.4 + 184.382

minimum cost ≈ 368.78 dollars