and what is the largest total area that can be enclosed is _____ Homework: Secti

Question

and what is the largest total area that can be enclosed is _____

Homework: Section 2.5: Optimization Score: 0.25 of 1 pt 20, 6 (5 complete) Gen Interest 2.5.13 A company plans to enclose three paraliel rectangular aroas for sorting retumed goods. The three areas are within one largo rectangular area and 1200 yd of fencing is available. What is the largest total area that can be enclosed? Seiect the correct choice below and fil in the answer box(es) to complete your choice. A. B. The length of each side of the larger rectangular area is he same and measures yd. The length of the shorter side of the larger rectangular area s d rd the length of the longer side of the larger rectangle' yd

Explanation / Answer

length =x yard

width = y yard

Since total fencing is of 1200,

2x +4y = 1200

x +2y= 600

x = 600 -2y

Now find area as

A=xy

=(600-2y)y

=600y-2y²

Find derivative and set to 0

A' =0

600-4y =0

4y =600

y =600/4

y= 150

hence

x = 600 -2 *150= 300

Area =x*y= 300 *150 = 45000

Thus, Option B is correct

length of shorter side = 150

length of longer side = 300

Area = 45000

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