Answer: 15 boxes
Step-by-step explanation:
From the question, we are informed that Denise wants to cover a 21.75 square foot wall with weathered wood and that each box of weathered wood contains 1.5 square feet of wood.
The number of boxes of weathered wood that she need will be calculated by dividing 21.75 square feet by 1.5 square feet. This will be:
= 21.75/1.5
= 14.5
= 15 boxes approximately
A = first piece, b = second piece, c = third piece
a + b + c = 47
b = 3a
c = 5a + 2
a + (3a) + (5a + 2) = 47.....combine like terms
9a + 2 = 47
9a = 47 - 2
9a = 45
a = 45/9
a = 5 ft
b = 3a.....b = 3(5)....b = 15 ft
c = 5a + 2....c = 5(5) + 2.....c = 25 + 2....c = 27 ft
longest piece (c) = 27 ft
Answer:
C(p) = 4,96 (in thousands of dollars)
l = 2980 $ invest in labor
k = 2980 $ invest in equipment
Step-by-step explanation:
Information we have:
Monthly output P = 450*l*k ⇒ k = P/450*l
But the production need to be 4000
Then k = 4000/450*l
Cost of production = l * k (in thousands of dollars)
C(l) = l + 4000/450*l
Taking derivatives (both members of the equation)
C´(l) = 1 - 400 /45*l² ⇒ C´(l) = 0 ⇒ 1 - 400/45l² = 0
45*l² - 400 = 0 ⇒ l² = 400/45
l = 2.98 (in thousands of dollars)
l = 2980 $ And
k = 400/45*l ⇒ k 400/45*2.98
k = 2.98 (in thousands of dollars)
C(p) = l + k
C(p) = 2980 + 2980
C(p) = 5960 $
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