Please help! A rectangular area adjacent to a river is to be fenced in, but no fencing is required on the side by the river. The total area to be enclosed is 1000 square feet. Fencing for the side parallel to the river is $7 per linear foot, and fencing for the other two sides is $3 per linear foot. The four corner posts cost $35 apiece. Let x be the length of the one the sides perpendicular to the river.
Find a cost equation C(x).
Find the minimum cost to build the enclosure.

Question

Please help! A rectangular area adjacent to a river is to be fenced in, but no fencing is required on the side by the river. The total area to be enclosed is 1000 square feet. Fencing for the side parallel to the river is $7 per linear foot, and fencing for the other two sides is $3 per linear foot. The four corner posts cost $35 apiece. Let x be the length of the one the sides perpendicular to the river.
Find a cost equation C(x).
Find the minimum cost to build the enclosure.

thomas5267 · Answer

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Let the length of the side parallel to river be y and the length of the side perpendicular to the river be x.  The constraint is xy=1000.  Try construct a cost function.