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Question

To enclose a yard, a fence is built against a large building, so that fencing material is used only on three sides. Material for the ends costs $15 per ft; material for the side opposite the building costs$25 per ft. Find the dimensions of the yard of maximum area that can be enclosed for $2400.

Solution

VerifiedAnswered 6 months ago

Answered 6 months ago

Step 1

1 of 4Using Lagrange MuItipIiers $\\$ ($z=f(x, y)$, subject to the constraint$$\mathrm{g}$(x, y)=0$)\\

- Write the constraint in the form$g(x, y)=0. $2. Form the Lagrange function$F(x, y, \lambda)=f(x, y)-\lambda\cdot g(x, y). $3. Find$F_{x}(x, y, \lambda), F_{y}(x, y, \lambda)$, and$F_${\lambda}$(x, y, \lambda). $4. Form the system of equations$ F_{x}(x, y, \lambda)=0, F_{y}(x, y, \lambda)=0$, and$F_${\lambda}$(x, y, \lambda)=0. $5. Solve the system in Step 4.$ $The relative extrema for$f$ are among the solutions of the system.

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