Answer:
We conclude that a dimension of the yard
17·25=425
Step-by-step explanation:
We know that the farmer has a total of 1950 dollars to spend on the project. Also we know that fence for side parallel to the barn will cost 55 per foot and the fence for the other two sides will cost 20 per foot.
We conclude that the farmer must fence one side parallel to the barn will cost 55 per foot, and the fence for the other two sides will cost 20 per foot.
We get
55+2·20=55+40=95
The farmer has a total of 1950 dollars, we have
1950:95=20.52
As the other two sides are cheaper to build, then they will be longer than the side parallel to a barn.
We conclude that the dimensions for the yard that will have the largest area
25 foot whic cost 20 per foot
17 foot whic cost 55 per foot
We get:
17·55+2·(25·20)=935+1000=1935 < 1950
We conclude that a dimension of the yard
17·25=425
Answer:
The dimension should be 17.73ft by 24.37ft
Step-by-step explanation:
The area of a rectangle is given as;
A = L×B ....1
The fence would have three sides
L = a length parallel to the barn
2B = the two other sides
Total cost = 1950
Total cost of fencing the yard;
55L + 20(2B) = 1950
Making B the subject of formula
B = (1950-55L)/40 ....2
Substituting eqn 2 into eqn 1
A = L × (1950-55L)/40
A = (1950L - 55L^2)/40 ....3
Therefore, at maximum area, dA/dL = 0
Differentiating equation 3;
dA/dL = (1950-110L)/40 = 0
1950 -110L = 0
L = 1950/110
L = 17.73ft
Substituting the value of L into equation 2
B = (1950-55(17.73))/40
B = 24.37ft
Therefore, the length parallel to the barn should be 17.73ft and the other two sides should be 24.47ft each.
Confirmation;
Area = 17.73 × 24.37 = 432.1ft^2
Cost = 17.73×55 + 24.37(2×20) = 1949.95 </= 1950 dollars.
Confirmed
