Answer:
Length l = 15 - 2x = 15 - 2(1.5) = 12.00 in
Breadth b = 7 - 2x = 7 - 2(1.5) = 4.00 in
Height h = x = 1.50 in
Step-by-step explanation:
The volume of a box can be written as;
V = l×b×h
Where;
Length = l
Breadth = b
Height = h
Let x represent the length of the cube cut out of the four edges.
Using the attached image;
Length l = 15 - 2x
Breadth b = 7 - 2x
Height h = x
Substituting the values to the volume equation;
V = (15-2x)(7-2x)(x)
V = 105x - 30x^2 - 14x^2 + 4x^3
V = 105x - 44x^2 + 4x^3
At Maximum volume, V' = dV/dx = 0
V' = 105 - 88x + 12x^2 = 0
Solving the quadratic equation, we have;
x = 5.83 or x = 1.50
x cannot be 5.83 since 2x > 7 (greater than the breadth of cardboard)
Therefore ;
Length l = 15 - 2x = 15 - 2(1.5) = 12.00 in
Breadth b = 7 - 2x = 7 - 2(1.5) = 4.00 in
Height h = x = 1.50 in
