A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $5 per ft2 for the top, and $4 per ft2 for the sides. Find the box of greatest volume that can be constructed for $204. Round your answer to 2 decimals. slader -g

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=

b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation:

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58