A rectangular storage container with an open top is to have a volume of 10 m3. T

Question

A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)

$___

Explanation / Answer

let the width be w => the length would be l= 2w and height be h given volume of the container = 10 => 4h(w^2) = 10 Area of the base = lw=(2w)w= 2w^2 and area of the sides = 2(lh)+2(wh) = 6wh base costs $10 per square meter implies cost for the base = 20(w^2) and cost for the sides = $6x 6(wh) = 36wh the total cost = 20(w^2)+36(wh) volume of the container = 4h(w^2)=10 and h = 2.5/(w^2) => total cost = 20(w^2)+36x2.5/(w) = 20(w^2)+90/w for the cost to be minimum first differential should be zero => 40(w)-90/(w^2)=0 => w^3 = 9/4=2.25=> w=1.31 total cost = 20(w^2)+90/w=$103

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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