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tyairamifflin2411
21.04.2020 •
Mathematics
A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $3 per foot, while the remaining two sides will use standard fencing costing $2 per foot. The budget that will be entirely used for fencing is $6000. In order to maximize the area of the plot, how many feet of standard fencing should be purchased for the project?
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Ответ:
1700 ft
Step-by-step explanation:
Let the dimensions of the plot of land be x any y
Where:
x is fenced using heavy-duty fencing selling for $3 per footy is fenced using standard fencing costing $2 per foot.Perimeter of the Land=2x+2y
Cost of Fencing =$3(2x)+$2(2y)=6x+4y
The budget that will be entirely used for fencing is $6000.
Therefore: 6x+4y=6000Make x the subjectArea of the Land, A(x,y)=xy
Substitute
into A(x,y)
The Area is maximized when its derivative equals zero.
3000-4y=0
4y=3000
y=750
Recall:![x=\dfrac{6000-4y}{6}=\dfrac{6000-4(750)}{6}=\dfrac{6000-3000}{6}=500](/tpl/images/0615/9589/544dd.png)
Therefore: x=500ft, y=750ft
Since side y is fenced using standard fencing,
Feet of standard Fencing required = 2y=2 X 750 =1500 ft
Ответ:
30 people
Step-by-step explanation:
If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.