Answer:
V = 23.85 ft³
Step-by-step explanation:
The dimension of the square base = x ft by x ft
Height of box = y
Volume of the box,
Cost of top = $4 *
Cost of the bottom = $9 *
Cost of the sides = $3 * 4xy
Total cost = 4x² + 9x² + 12xy
Total cost = 13x² + 12xy
Total cost = $193
193 = 13x² + 12xy
But volume, V = x²y
V =
V = ...................(1)
At maximum value, V' = 0
0 =
x = 2.23
Put the value of x into (1)
V = 23.85 ft³