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  • 3 years ago

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.

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  1. campbell_st
    • 3 years ago
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    well draw a picture |dw:1367708620256:dw| 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 \[C(x) = 10x + \frac{8000}{x} + 100\]

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