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There are $756 available to build a fence around a rectangular garden. One side must be reinforced and will cost $17 per foot. The other three sides can be built for $10 per foot. Find the dimensions of the largest possible garden which can be built under these constraints.

The reinforced wall will be

The other dimension is

The resulting area is

2007-12-02 09:48:33 · 1 answers · asked by Nidhi M 1 in Science & Mathematics Mathematics

1 answers

The sides of the garden wall are L and W.

The cost is

756 = ( 17 ) ( W ) + ( 10 ) ( W + 2 L )

The area is

A = LW

You wish to maximize A, so we need a substitution for either L or W. Create this from the cost equation; then you'll have an equation with only one variable (L or W). Take the first derivative of that equation with respect to the variable, set it equal to zero, and solve to get the L or W that maximizes the area.

2007-12-02 09:54:51 · answer #1 · answered by jgoulden 7 · 0 0

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