A rectangle with the length of 1/5 yard and the width of 2/3 yards
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Answer:
Step-by-step explanation:
Let
Side of square base=x
Height of rectangular box=y
Area of square base=Area of top=
Area of one side face=
Cost of bottom=$9 per square ft
Cost of top=$5 square ft
Cost of sides=$4 per square ft
Total cost=$204
Volume of rectangular box=
Total cost=
Substitute the values of y
Differentiate w.r.t x
It takes positive because side length cannot be negative.
Again differentiate w.r. t x
Substitute the value
Hence, the volume of box is maximum at x=2.2 ft
Substitute the value of x
Greatest volume of box=