Find the volume. The cabinet that will enclose the Arsenic model D loudspeaker s

Question

Find the volume.

The cabinet that will enclose the Arsenic model D loudspeaker system will be rectangular and will have an internal volume of 2.4 ft3. For aesthetic reasons, the design team has decided that the height of the cabinet is to be 1.5 times its width. If the top, bottom, and sides of the cabinet are constructed of veneer costing 75C/square foot and the front (ignore the cutouts in the baffle) and rear are constructed of particle board costing 25C/square foot, what are the dimensions of the enclosure that can be constructed at a minimum cost?

Explanation / Answer

V = 2.4
h = 1.5w

V = L * w * h
2.4 = L * w * (1.5w)
L = 2.4 / (1.5w^2)

A = 2Lw + 2Lh + 2wh

Uh... Question... which side is the front/back? >.< Lh or wh?

*assuming wh is the front/back*

C = 40(2Lw + 2Lh) + 20(2wh)
C = 80(Lw + Lh) + 40(wh)
C = 80( 2.4 / (1.5w^2) * w + 2.4 / (1.5w^2) * 1.5w) + 40(w * 1.5w)
C = 80( 2.4 / (1.5w) + 2.4 / w) + 40(1.5w^2)
C = 192( 1/(1.5w) + 1/w) + 60w^2
C = 128/w + 192/w + 60w^2
C = 60w^2 + 320/w
C' = 120w - 320/w^2
320/w^2 = 120w
320 = 120w^3
w^3 = 8/3
w = 1.387 ft.
h = 2.080 ft.
L = 0.832 ft.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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