7. 0 +-6.25 points LarCalcET6 13.9.009 My Notes Ask Your Teacher O A home improv

Question

7. 0 +-6.25 points LarCalcET6 13.9.009 My Notes Ask Your Teacher O A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 218.75 cubic feet. The cost of wall paint is $0.04 per square foot and the cost of ceiling paint is $0.14 per square foot. Find the room dimensions that result in a minimum cost for the paint. sides height ft ft What is the minimum cost for the paint? (Round your answer to two decimal places.) Need Help? Read It Talk to a Tutor

Explanation / Answer

Let l be be the sides and h be the height

V= l2h

218.75=l2h

h= 218.75/l2

C= 4 * 0.04 * l h +0.14 *l2

C= 0.16*(218.75/l)+0.14 l2 = 35/l + 0.14l2

C' = -35/l2+ 0,28l

C'=0

0.28l = 35/l2

l3=125

l=5 feet

h=218.75/52=8.75ft

Sides = 5 feet

height = 8.75 feet

Minimum cost=(35/l)+0.14l2 =(35/5)+0.14(25)=$10.5

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.