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.

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.

campbell_st · Answer

well draw a picture 

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start with the area 

$$1000 = x \times l$$

make l the subject. 

$$l = \frac{1000}{x}$$

now the cost 

$$C(x) = 2\times x \times 5 + l \times 8 + 4 \times 25$$

substituting l from the area formula 

$$C(x) = 10x + \frac{8 \times 1000}{x} + 100$$

so your cost function in terms of x is 

$$C(x) = 10x + \frac{8000}{x} + 100$$