Homework Help: calculus

Posted by tiana on Sunday, January 2, 2011 at 2:20pm.

i understand optimization but im stuck on this problem.. mrs.day is building a new deck. she has 580 square feet to enclose. if one side is bounded by a wall, find the minimum cost to build the deck if one pair of opposite sides cost $12 per foot and remaining sides cost $19 per foot. what are the demisions of the deck?

calculus - Damon, Sunday, January 2, 2011 at 2:36pm
Is she building a deck or a railing around the deck.
From the wording I will assume a railing.
The two sides of the railing, length a, cost 12/ft each.
The front of the railing, length b, costs 19.ft

a*b = 580

2*12 a + 19 b = c, the cost

dc/da = 0 for min = 24 da/da +19 db/da
but
b = 580/a
db/da = -580/a^2
so
0 = 24 +19 (-580)/a^2
24 a^2 = 19*590
a^2 = 459
a = 21.4
then b = 27
Now it might be that the front cost 12 and the sides cost 19
in that case
2*19 a + 12 b = c
dc/da = 0 = 38 da/da + 12 db/da
db/da is still -580/a^2
38 = 12(580)/a^2
a^2 = 183
a = 13.5
then b = 42.8

Answer this Question

Related Questions

math - you are building a deck. you make a scale drawing with a scale of 2 feet=...
math - I don't understand this question so if you don't mind will you ...
geometry - A circular pool with a diameter of 32 feet is surrounded by a wood ...
Calculus - A ladder 15 feet long is leaning against a building so that end X is ...
math - The Ling family is building a deck on their house. It will run the length...
calculus - A multistoried building has a floor area of 2,000 square feet on the ...
Pre-Calculus - A rectangular garden with an area of 250 square meters is to be ...
Calculus Optimization Problem - Find two positive numbers whose sum is 15 such ...
Math - Julie is digging a square area in her backyard for a vegetable garden. If...
geometry - ye has 44 feet of fencing to enclose a rectangular garden. She wants ...

For Further Reading

First Name:
School Subject:
Answer: