Minimum Cost A rectangular area adjacent to a river is to be fenced in; no fence is needed on the river side. The enclosed area is to be 1000 square feet. Fencing for the side parallel to the river is $5 per linear foot, and fencing for the other two sides is $8 per linear foot; the four corner posts are $25 apiece.
Let x be the length of one of the sides perpendicular to the river.
(a)Write a function C(x) that describes the cost of the project.
(b)What is the domain of C

Question

Minimum Cost A rectangular area adjacent to a river is to be fenced in; no fence is needed on the river side. The enclosed area is to be 1000 square feet. Fencing for the side parallel to the river is $5 per linear foot, and fencing for the other two sides is $8 per linear foot; the four corner posts are $25 apiece. 
Let x be the length of one of the sides perpendicular to the river.
(a)Write a function C(x) that describes the cost of the project.
(b)What is the domain of C

anonymous · Answer

Qa 

If x is the side perpendicular to the river, 1000/x is the length parallel to the river. 

c = 8 * 2x + 5 * 1000/x + 4 * 25 

16x + 5000/x + 100 

------------------------- 

Qb 

c = 16 - 5000/x^2 , c = 19,000/x^3, minima at x = 25/√2, 

Minimum 100(1 + 4√2), ≈ 665.685 

No global maxima, eg for x = 1000, c = 16105 

For x = 10,000, c = 160,100.5 & so on. 

Domain [100(1+4√2) , oo) 

Shouldn't x be the independent variable, domain (0, oo) 

With the *range* of c being [100(1 + 4√2), oo)