A farmer wants to enclose 135000 square yards of land in a rectangular plot. The material used for the front side costs $2 per yard, the material for the other three sides costs $1 per yard. Determine the dimensions that will minimize cost.

Question

anonymous · Answer

ok i have gotten as far as:  3-(270000/y^2) = 0 do I solve for y?

anonymous · Answer

call the side that cost $1 , and the side that is $2 y, then you have a total cost is $C=2x+3y$ and you also know that $xy=13500$ and therefore $y=\frac{135000}{x}$
replace in first equation to get $$C(x)=2x+\frac{3\times 135000}{x}$$

anonymous · Answer

ok i screwed that up

anonymous · Answer

should be $$C=3x+2y$$
$$C(x)=3x+\frac{2\times 135000}{x}$$

anonymous · Answer

oh i see  you have gotten past this step and have taken the derivative and now just need to solve

anonymous · Answer

$$3-\frac{270000}{x^2}=0$$
$$\frac{270000}{x^2}=3$$
$$270000=3x^2$$
$$x^2=90000$$

anonymous · Answer

so $x=300$

anonymous · Answer

x=3000

anonymous · Answer

yes thats where i was confused satellite73

anonymous · Answer

i wasnt solving for y correctly

anonymous · Answer

y=45