Afarmer has $1500 available to build an e-shaped fence along a straight river so as to create two identical pastures. the materials for the side parallel to the river cost $6 per foot, and the materials for the three sections perpendicular to the river cost $5 per foot. find the dimensions for which the total area is as large as possible.

The largest dimensions that are possible would be 50 foot by 125 foot.

Step-by-step explanation:

Since we have given that

Amount a farmer has available = $1500

Let x be the side perpendicular to the river.

Let y be the side parallel to the river.

Number of section perpendicular to the river = 3

cost of material for the side parallel to the river = $6 per foot

Cost of material for the side perpendicular to the river = $5 per foot

So, total cost becomes

Area would be

Now, put A' = 0 to get the critical points.

So, it becomes,

so, at x= 50 it will give maximum dimensions.

So, the largest dimensions that are possible would be 50 foot by 125 foot.

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step-by-step explanation: