Question

NO LINKS!! Please help me with this problem.​

Answer 1

• 11.619 by 5.164 feet
• $464.76 minimum cost

Step-by-step explanation:

You want the dimensions and cost of a rectangular enclosure with an area of 60 square feet and 5 internal partitions. The cost of outside fence is $10 per foot, and the cost of partition fence is $5 per foot.

Setup

Let x represent the length of the enclosure, and y the width (and the partition length). Then we have ...

xy = 60

10(2x) = cost fencing for length

10(2y) +5(5y) = cost of fencing for width

We know the cost will be minimized when the cost of fence for the length is equal to the cost of fence for the width.

20x = 45(60/x)

Solution

x² = 135 . . . . . . . . . . . multiply by x/20

x = 3√15 ≈ 11.619 . . . .square root

y = 60/(3√15) = (4/3)√15 ≈ 5.164 . . . . . find y

Then the cost is ...

2(10(2x)) = 120√15 ≈ 464.76 . . . . minimum cost

The enclosure is 11.619 by 5.164 feet, for a cost of $464.76.

Answer 2

Answers:

Min cost = $464.76

Dimensions = 11.619 feet by 5.164 feet

Each value mentioned above is approximate.

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Step-by-step explanation:

x = horizontal dimension

y = vertical dimension

xy = 60

y = 60/x

The amount of outer fencing needed is 2x+2y feet, aka the perimeter of the largest rectangle.

There are 5 vertical inner fences, so we need 5y feet of inner fencing.

Let's set up the cost function.

Cost = 10*(amount of outer fencing) + 5*(amount of inner fencing)

C = 10*(2x+2y) + 5*(5y)

C = 20x+20y+25y

C = 20x+45y

Plug y = 60/x into the cost function.

C = 20x+45y

C = 20x+45(60/x)

C = 20x + (2700/x)

Then use either calculus or a graphing calculator to find the lowest point on the cost curve is roughly located at (11.619, 464.758)

Use the x value x = 11.619 to find its paired y value

y = 60/x

y = 60/11.619

y = 5.16395558998192

y = 5.164

The entire enclosure should be roughly 11.619 feet by 5.164 feet

The total cost is minimized at approximately $464.76