a. You have $2000 dollars to buy fence to enclose a rectangular plot of land (se

Question

a. You have $2000 dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom costs $5 per foot and for the sides it costs $2 per foot. Find the dimensions, x and y, of the plot with the largest area. For this largest plot, how much money was used for the top and bottom, x, and for the sides, y? b. You have T dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom costs $5 per foot and for the sides it costs $2 per foot. Find the dimensions of the plot with the largest area. For this largest plot, how much money was used for the top and bottom, x, and for the sides, y? c. You have T dollars to buy fence to enclose a rectangular plot of land. The fence for the top and bottom costs $A per foot and for the sides it costs $B per foot. Find the dimensions of the plot with the largest area. For this largest plot, how much money was used for the top and bottom, x, and for the sides, y?

Explanation / Answer

I have solved this question earlier with different figures. Please workout using yours figures. If you need any further help just PM me. If I have helped you please rate me 5 stars first (before you rate anyone else)

a. you have $2000 dollars to buy fence to enclose a rectangular plot of land. The fence for the top and bottom costs $5 per foot and for the sides it costs $2 per foot. Find the dimensions, x and y, of the plot with the largest area. For this largest plot, how much money was used for the top and bottom, x, and for the sides, y?

b. you have G dollars to buy fence to enclose a rectangular plot of land. The fence for the top and bottom costs $5 per foot and for the sides it costs $2 per foot. Find dimensions of the plot with the largest area. For this largest plot, how much money was used for the top and bottom,x,and for the sides, y?

c. you have H dollars to buy fence to enclose a rectangular plot of land. The fence for the top and bottom costs $A per foot and for the sides it costs $B per foot. Find dimensions of the plot with the largest area. For this largest plot, how much money was used for the top and bottom, x, and for the sides, y?

answer

a) let x be length of top and y be length of sides then cost required will be = 5x + 5x + 2y + 2y

then our equation will be 10x + 4y = 2000

and we need to maximize area that is xy since its a rectangle

then y = (2000 - 10x)/4

put value of y in area equation then eqn of area will be = x(2000 - 10x)/4

differentiate above with respect to x for maximum

Hence x = 100 and y = 250

b) similarly like above eqn will be 10x + 4y = G

then area = xy

replace value of y from eqn in area xy

then area will be = x(G - 10x)/4

differentiate with respect to x and equate to 0 for maxm will give x = G/20 then y = G/8

c) similarly eqn => 2A + 2B = H

area = > AB using same conditions for maximizing area we get

A = H/4 and B = H/4

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.