Abox is to be made where the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is $0.05per square foot. find the dimensions of a box with volume 15cubic feet that has minimum cost.

Let the width of the base be x and the height of the box be y. The base is a square so its area is x2. Then the volume of the box is "base area times height", so the volume is V=x2y=40ft3.

The area of the base is x2, so the cost of the base is 0.31x2.

The area of each side is xy, so the cost of each side is 0.05xy, so the cost of all four sides is 4×0.05xy=0.2xy.

The area of the top is x2, so the cost of the top is 0.19x2.

So the total cost is C=0.31x2+0.19x2+0.2xy=0.5x2+0.2xy.

Since x2y=40, we have y=40/x2, so C=0.5x2+0.2x×40x2=0.5x2+8x. This we can optimise using derivatives.

Step-by-step explanation:

step-by-step explanation: the answer is 27. first multiply .32 by 25 which equals 8. then add 8 to 25 which gives you 33. then you subtract that from 6 since she gave 6 to her brother.

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step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

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m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0